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- Triangle KLB

It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o - Top of the tower

The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint - Triangle

Can be rectangular triangle equilateral? - Similarity coefficient

The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of the larger triangle. - Funnel

The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water. - EQL triangle

Calculate inradius and circumradius of equilateral triangle with side a=77 cm. - Internal angles

The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete - Triangle eq

Calculate accurate to hundredths cm height of an equilateral triangle with a side length 12 cm. Calculate also its perimeter and content area. - Prism - eq triangle

Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm. - Octahedron

All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron. - Candy - MO

Gretel deploys to the vertex of a regular octagon different numbers from one to eight candy. Peter can then choose which three piles of candy give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles trian - The perimeter

The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX? - Rectangular trapezoid

The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the - The plaster cast

The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area. - Eq triangle minus arcs

In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts - Triangular pyramid

A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm - The funnel

The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel. - Triangular pyramid

Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm. - Triangles

Equilateral triangle with side 40 cm has the same perimeter as an isosceles triangle with arm of 45 cm. Calculate the base x of an isosceles triangle. - Pentagon

Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch. - Rhombus

ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. - Equilateral triangle ABC

In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont - Infinite sum of areas

Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tr - Boat

A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight? - Climb

Road has climbing 1:27. How big is a angle corresponds to this climbing? - Cone

Circular cone of height 15 cm and volume 5699 cm^{3}is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut. - Rectangular triangles

The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 - Count of triangles

Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points. - Climb

On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went? - Similarity

Are two right triangles similar to each other if the first one has a acute angle 70° and second one has acute angle 20°? - Reverse Pythagorean theorem

Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ? - Railways

Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters. - See harmonics

It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases. - Geodesist

Triangle shaped field (triangle ABC) has side AB = 129 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area. What will be the length of the path XY? Help please geodesist ... - Hexagon

There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply.... - Cosine

Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544. - Combi-triangle

On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square? - Two triangles SSA

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14 - Matches

George poured out of the box matches and composing them triangles and no match was left. Then he tries squares, hexagons and octagons and no match was left. How many matches must be at least in the box? - Octagon from rectangle

From tablecloth rectangular shape with dimensions of 4 dm and 8 dm we cuts down the corners in the shape of isosceles triangles. It thus formed an octagon with area 26 dm^{2}. How many dm^{2}we cuts down? - Traffic laws

Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa - Right triangles

How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality). - MO - triangles

On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB seg - Similarity

ABC is a triangle wherein a = 4 cm, b = 6 cm, c = 8 cm. Is it similar to the triangle DEF: d = 3 cm, e = 4.5 cm, f = 6 cm? If so, determine the ratio of similarity. - Inclined plane

On the inclined plane with an angle of inclination of 30 ° we will put body (fixed point) with mass 2 kg. Determine the acceleration of the body motion on an inclined plane. - TV diagonal

Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9? - Triangles

Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3' - Trapezoid IV

In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD? - Similarity of squares

The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ? - Diagonal in rectangle

In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts. - Area and two angles

Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°. - Shadow and light

Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall? - Isosceles trapezoid

In an isosceles trapezoid KLMN intersection of the diagonals is marked by the letter S. Calculate the area of trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm^{2}. - Airplane

Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies? - Euclid theorems

Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm. - Sides ratio

Calculate the circumference of a triangle with area 84 cm^{2}if a:b:c = 10:17:21 - Lighthouse

The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lighth - Angle in RT

Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions. - Tree shadow

Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree? - Ruler

How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm. - Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current heig - Tree shadow

The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)? - V-belt

Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm - Sides od triangle

Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm. - Quadrilateral 2

Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles. - Hexagonal prism

The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism. - Hexagon cut pyramid

Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm. - Thales

Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm as shown. Calculate the depth of the hole. - Display case

Place a glass shelf at the height of 1m from the bottom of the display case in the cabinet. How long platter will we place at this height? The display case is a rectangular triangle with 2 m and 2.5 m legs. - Similarity coefficient

The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ". - Mirror

How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m. - Type of triangle

How do I find the triangle type if the angle ratio is 2:3:7 ? - Garage

There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the garag - MO Z9–I–2 - 2017

In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm^{2}. Find the area of the entire trapezoid. - Surface area 6

Find the surface area of a prism whose bases are right triangles with sides of length 3, 4, and 5 inches and a height of 8 inches. Include a sketch - Shadow of tree

Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters? - Triangles

Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm and the length of the third side is expressed in whole centimeters. How many triangles does he have? - A boy

A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff. - Triangles

Hanka cut the 20 cm long straws into three pieces each piece had a length in cm. Then, with these three pieces, she tried to make a triangle. a) What circuit has each of the triangles? b) How long can the longest side measure? c) How many different triang - Adding shapes

5 triangles + 1 square = how many sides in all - Area of iso-trap

Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other. - Triangles

Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle? - Two angles

The triangles ABC and A'B'C 'are similar. In the ABC triangle, the two angles are 25° and 65°. Explain why in the triangle A'B'C 'is the sum of two angles of 90 degrees. - Shadow

A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house? - Nonagon

Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm - Pyramid cut

We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm^{2}. Find the area of the - Rectangle diagonal

The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm^{2}. - Mast shadow

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines. - Diagonals at right angle

In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD? - Trapezium diagonals

It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC. - Lighthouse

Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea - Right circular cone

The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base. - Two chords

Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle. - Secret treasure

Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure. - Sides of right angled triangle

One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Diagonal intersect

isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles? - Conical bottle

When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? - Similarity of two triangles

The KLM triangle has a side length of k = 6.3cm, l = 8.1cm, m = 11.1cm. The triangle XYZ has a side length of x = 8.4cm, y = 10.8cm, z = 14.8cm. Are triangle KLM and XYZ similar? (write 0 if not, if yes, find and write the coefficient of a similarity) - Similarity coefficient

In the triangle TMA the length of the sides is t = 5cm, m = 3.5cm, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other. - Lookout tower

Calculate the height of a lookout tower forming a shadow of 36 m if at the same time a column 2.5 m high has a shadow of 1.5 m. - The triangles

The triangles KLM and ABC are given, which are similar to each other. Calculate the lengths of the remaining sides of the triangle KLM, if the lengths of the sides are a = 7 b = 5.6 c = 4.9 k = 5 - Cutting cone

A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm. - An observer

An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower? - Similar triangles

In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D´E´F´ is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D´E´F´ if the similarity coefficient is one-seventh. - Similar triangles

The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm - The triangles

The triangles ABC and A'B'C 'are similar with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '. - Similar triangles

Triangle A'B'C 'is similar to triangle ABC, whose sides are 5 cm, 8 cm, and 7 cm long. What is the length of the sides of the triangle A'B'C ' if its circumference is 80 cm? - Chimney and tree

Calculate the height of the factory chimney, which casts a shadow 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long. - Inclined plane

The body stays on an inclined plane and exerts a compressive force of 70N on it. Find the angle between the inclined plane and the horizontal if a gravitational force of 100N acts on the body. - Distance of points

A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - Poplar shadow

The nine-meter poplar casts a shadow 16.2 m long. How long does a shadow cast by Peter at the same time, if it is 1.4 m high? - Vertical rod

The vertical one meter long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long at the same time. - A cliff

A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high and meets the ground at a point 8 ft from the base of the pole. If the point is 93 ft from the base of the cliff, how high is the cliff? - Maximum area of rhombus

Calculate the interior angles at which equilateral rhombus has a maximum area. - Equilateral triangle

Calculate the side of an equilateral triangle, if its area is 892 mm^{2}. - Height 2

Calculate the height of the equilateral triangle with side 38. - Axial section

Axial section of the cone is an equilateral triangle with area 168 cm^{2}. Calculate the volume of the cone. - Equilateral triangle

How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it? - Height

Calculate height of the equilateral triangle if its perimeter is 8? - Height UT

How long is height in the equilateral triangle with a side b = 43? - Semicircle

In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC? - Circle section

Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector and - Equilateral cylinder

Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm^{3}. Calculate the surface area of the cylinder. - Equilateral triangle v2

Equilateral triangle has a perimeter 36 dm. What is its area? - Triangular prism - regular

The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism. - Equilateral triangle v3

Calculate the content of the colored gray part. Equilateral triangle has side length 8 cm. Arc centers are the vertices of a triangle. - Prism

Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m. - Axial cut

The cone surface is 388.84 cm^{2}, the axial cut is an equilateral triangle. Find the cone volume. - Equilateral cone

We pour so much water into a container that has the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Equilateral triangle

The equilateral triangle has a 23 cm long side. Calculate its content area. - Triangular prism

Calculate the surface of a triangular prism with the base of an equilateral triangle with a side length of 7.5 cm and a corresponding height of 6.5 cm. Prism height is 15cm. - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Calculate

Calculate the length of a side of the equilateral triangle with an area of 50cm^{2}. - Equilateral triangle

Calculate the area of an equilateral triangle with circumference 72cm. - Triangular prism

Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm - Equilateral cylinder

A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - An equilateral

An equilateral triangle with a side 10 m represents a wooden platform standing in a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat? - An equilateral triangle

The perimeter of an equilateral triangle is 33cm. How long is each side? - Three parallels

The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - Perimeters

A rectangle has a perimeter of 16p centimeters, it had a width of 2p centimeters. Each side of an equilateral triangle is 1/2 the length of the rectangle. Find the total perimeter of the rectangle and the triangle if p=8. - An equilateral

An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Volume ratio

Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone. - The sides 3

The sides of an equilateral triangle are 9.4 cm, correct to the nearest one decimal place. Work out the upper bound of the side of this triangle - Cone

Calculate volume and surface area of the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°. - n-gon

What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm? - n-gon II

What is the side length of the regular 5-gon circumscribed circle of radius 11 cm? - Tower

How many m^{2}of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°? - Road

The angle of a straight road is approximately 12 degrees. Determine the percentage of this road. - Tent

Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m. - Right triangle

Calculate the missing side b and interior angles, perimeter and area of a right triangle if a=10 cm and hypotenuse c = 16 cm. - Crossroads

Passenger car and an ambulance come to the rectangular crossroad, the ambulance left. Passenger car at speed 39 km/h and ambulance at 41 km/h. Calculate such a relative speed of the ambulance move to the car. - Right triangle Alef

The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs. - Rotation of the Earth

Calculate the circumferential speed of the Earth's surface at a latitude of 61°. Consider a globe with a radius of 6378 km. - Slope of track

Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitrianske Pravno (354 m AMSL), if the track is 11 km long. - Triangle SSS

Calculate perimeter and area of a triangle ABC, if a=53, b=46 and c=40. - N-gon angles

What is the sum of interior angles 8-gon? What is the internal angle of a regular convex 8-polygon? - Diagonals

Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°. - Trapezoid

Calculate area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm.. - Ladder

Ladder 8 m long is leaning against the wall. Its foot is 1 m away from the wall. In which height ladder touches the wall? - The ladder

The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall? - Cube diagonal

Determine the length of the cube diagonal with edge 37 mm. - Square and circles

Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles. - Triangle SAA

The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle. - Rhombus

Calculate the perimeter and area of a rhombus whose diagonals are 39 cm and 51 cm long. - Cube - angles

Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base. - Isosceles III

The base of the isosceles triangle is 17 cm area 416 cm^{2}. Calculate the perimeter of this triangle. - Square diagonal

Calculate the length of the square diagonal if the perimeter is 476 cm. - Circle in rhombus

In the rhombus is inscribed circle. Contact points of touch divide the sides to parts of length 19 cm and 6 cm. Calculate the circle area. - Circle chord

What is the length x of the chord circle of diameter 115 m, if the distance from the center circle is 11 m? - Triangle SAS

Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °. - Road

Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B. - Rhombus ABCD

Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD. - Angles in triangle

The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle? - Triangle ABC

Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle h_{AB}to the side AB. - Kites

Boys run kite on a cable of 68 meters long. What is the kite altitude, if the angle from the horizontal plane is 72°? - Rectangular trapezoid

How many inner right angles has a rectangular trapezoid? - Circles

Three circles of radius 95 cm 78 cm and 64 cm is mutually tangent. What is the perimeter of the triangle whose vertices are centers of the circles? - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel. - RT - hypotenuse and altitude

Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments? - Tangents

To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre. - Triangle angles

The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles. - Angles

The outer angle of the triangle ABC at the vertex A is 114°12'. The outer angle at the vertex B is 139°18'. What size is the internal angle at the vertex C? - Glass mosaic

How many dm^{2}glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%. - Cap

Jesters hat is shaped by a rotating cone. Calculate how much paper is needed to the cap 54 cm high when the head circumference is 47 cm. - Widescreen monitor

Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous than - Tetrahedral pyramid

Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm. - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 377 cm. - Right triangle

Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle. - Descent of road

Road sign informs the gradient is 10.3%. Calculate the angle which average decreases. - Median

The median of the triangle LMN is away from vertex N 84 cm. Calculate the length of the median, which start at N. - Circle

On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN. - ABS CN

Calculate the absolute value of complex number -15-29i. - Chord MN

Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle. - Steeple

Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high? - Building

The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building? - Cable car

Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope? - Triangle

Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33. - Right triangle

Right triangle legs has lengths 630 mm and 411 dm. Calculate the area of this triangle. - Heron backlaw

Calculate missing side in a triangle with sides 17 and 34 and area 275. - Sphere cuts

At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2. - Track arc

Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)? - V-belt

Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm. - Triangle and its heights

Calculate the length of the sides of the triangle ABC, if v_{a}=5 cm, v_{b}=7 cm and side b is 5 cm shorter than side a. - Angles

The triangle is one outer angle 158°54' and one internal angle 148°. Calculate the other internal angles of a triangle. - Isosceles triangle

Calculate the perimeter of isosceles triangle with arm length 73 cm and base length of 48 cm. - Median

In the right triangle are sides a=41 dm b=42 dm. Calculate the length of the medians t_{c}to the hypotenuse. - River

Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL. - Estate

Estate shaped rectangular trapezoid has bases long 34 m , 63 m and perpendicular arm 37 m. Calculate how long is its fence. - Box

Calculate the angle between box base 9 x 14 and body diagonal length 18. - Roof angle

The roof of the house has the shape of an isosceles triangle with arms 4 m long and the size of the base 6 m. How big an angle alpha does its roof make? - Center

Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18]. - Rhombus OWES

OWES is a rhombus given that OW 6cm and one diagonal measures 8cm. Find its area? - Is right?

Is triangle with sides 51, 56 and 77 right triangle? - Triangle

Determine if it is possible to construct a triangle with sides 28 31 34 by calculation. - Chord

In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord? - Euclid2

In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle. - Chord

Point on the circle is the end point of diameter and end point of chord length of radius. What angle between chord and diameter? - Diagonal

Can a rhombus have the same length diagonal and side? - 3-bracket

May be the largest angle in the triangle less than 20°? - 3-bracket 2

May be the smallest angle in the triangle greater than 70°? - 3-bracket 3

Two angles in a triangle are 90° and 60°. Has triangle at least two equal sides? - Diagonal

Can be a diagonal of diamond twice longer than it side? - Diagonals of the rhombus

Calculate height of rhombus whose diagonals are 12 cm and 19 cm. - Center traverse

It is true that the middle traverse bisects the triangle? - Trigonometric functions

In right triangle is: ? Determine the value of s and c: ? ? - Regular 5-gon

Calculate area of the regular pentagon with side 7 cm. - Rotation

The right triangle with legs 11 cm and 18 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone. - Felix

Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km. - Octagon

We have a square with side 84 cm. We cut the corners to make his octagon. What will be the side of the octagon? - Elevation

What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km. - Height

Is right that in any right triangle height is less or equal half of the hypotenuse? - Square

Calculate area of the square with diagonal 64 cm. - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Circles 2

Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm. - SAS triangle

The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle. - Angle

Draw angle |∠ ABC| = 130° and built its axis. What angle is between axis angle and arm of angle? - Triangle

Prove whether you can construct a triangle ABC, if a=9 cm, b=6 cm, c=10 cm. - Triangle P2

Can triangle have two right angles? - Common chord

Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles? - Rectangle

In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle? - Euclid1

Right triangle has hypotenuse c = 27 cm. How large sections cuts height h_{c}=3 cm on the hypotenuse c? - Euklid4

Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle. - Right triangle

Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides. - Triangle ABC

Calculate the sides of triangle ABC with area 1404 cm^{2}and if a: b: c = 12:7:18 - Sea

How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km). - Mast

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast, if the sun above the horizon is at angle 45°12'. - Triangle

Calculate the area of right triangle ΔABC, if one leg is long 14 and its opposite angle is 59°. - R triangle

Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - Rhomboid

Calculate the circumference and area of the rhomboid with sides 20 and 14, with their angle 50°. - Area 4gon

Calculate area of 4-gon, two and the two sides are equal and parallel with lengths 11, 5, 11 and 5. Inner angles are 45°, 135°,45°, 135°. - Pentagon

Calculate the area of regular pentagon, which diagonal is u=17. - Midpoints

Triangle whose sides are midpoints of sides of triangle ABC has a perimeter 45. How long is perimeter of triangle ABC? - Square diagonal

Calculate the length of diagonal of the square with side a = 23 cm. - Pyramid roof

2/4 of area of the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered? - Euclid3

Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg c_{b}= 39 cm. - Right isosceles

Calculate area of the isosceles right triangle which perimeter is 41 cm. - Greatest angle

Calculate the greatest triangle angle with sides 197, 208, 299. - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. Calculate the volume of a cone. - Diagonal

Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm^{2}. - Triangle TBC

TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB? - Gimli Glider

Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long it takes to plane from engine failure to hit the ground. Cal - Square

Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD. - Square 2

Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD. - Steps

How many steps you save if you go square estate for diagonal (crosswise), rather than circumvent on the two sides of its perimeter with 307 steps. - Area of RT

In the right triangle has orthogonal projections of legs to the hypotenuse lengths 7 cm and 12 cm. Determine the area of this triangle. - Movement

From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling. - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - Area of RT 2

Calculate the area of right triangle whose legs have a length 5.8 cm and 5.8 cm. - Described

Calculate perimeter of the circle described by a triangle with sides 478, 255, 352. - Cuboid

Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm^{3}. Calculate the length of the other edges. - Laws

From which law follows directly the validity of Pythagoras' theorem in the right triangle? ? - Hypotenuse and height

In a right triangle is length of the hypotenuse c = 56 cm and height h_{c}= 4 cm. Determine the length of both trangle legs. - Area of RT

Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5. - Right Δ

A right triangle has the length of one leg 11 cm and length of the hypotenuse 61 cm. Calculate the height of the triangle. - Trapezoid MO

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Canopy

Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m^{2}? - Rhombus

It is given a rhombus of side length a = 19 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 5 cm and a_{2}= 14 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Rectangle

In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?. - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 21 cm and t_{b}=12 cm. - Earth's circumference

Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes. - Center

In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z]. - IS trapezoid

Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm. - Circumferential angle

Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC. - R Trapezium

Rectangular trapezium has bases 12 and 5 and area 84 cm^{2}. What is its perimeter? - Rhombus

Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus? - Short cut

Imagine that you are going to the friend. That path has a length 120 meters. Then turn doprava and go another 630 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field? - IS triangle

Calculate interior angles of the isosceles triangle with base 40 cm and legs 22 cm long. - Slope

What is the slope of a line with an inclination 6.06 rad? - Garden

Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden? - Triangle in circle

Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC. - Logs

Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm? - Rectangle

The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle. - Recursion squares

In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm. Calculate: a) the sum of perimeters of all s - Infinity

In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares. - Building

How high is the building that throws horizontal shadow 95.4 m long at angle 50°? - River

From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river. - Distance

Calculate distance between two points X[18; 19] and W[20; 3]. - Stairway

What angle rising stairway if step height in 20 cm and width 26 cm? - Slope of the pool

Calculate slope (rise:run) of the bottom of swimming pool long 30 m. Water depth at beginning of pool is 1.13 m (for children) and depth at end is 1.84 m (for swimmers). Slope express as percentage and as angle in degrees. - Prism

The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism? - Side c

In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c. - Acute angles

Sizes of acute angles in the right-angled triangle are in the ratio 1: 3. What is size of the larger of them? - Observer

The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from the another end of the fence? - Triangle

For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle? - It is rectangular?

Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle? - Two boats

Two boats are located from a height of 150m above the surface of the lake at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the surface of the lake. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16? - 4s pyramid

Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height? - Reflector

Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane? - Sines

In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ) - OK circle

Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17. - Aircraft

The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements. - Circumscribing

Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm. - Height difference

What height difference overcome if we pass road 1 km long with a pitch21 per mille? - QuizQ

An isosceles triangle has two sides of length 7 km and 39 km. How long is a third side? - Hexagon

Draw a regular hexagon inscribed in a circle with radius r=8 cm. What is its perimeter? - Segment

Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5]. - Overload

Calculate how many g's (gravity accelerations) feel glider pilot when turning the horizontal circles of radius 148 m flying at 95 km/h. Centripetal acceleration is proportional to the square of the speed and inversely proportional to the radius of rotatio - Vector

Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2). - Rhombus and inscribed circle

It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals. - Square2

Side of the square is a = 6.2 cm, how long is its diagonal? - Road

Average climb of the road is given by ratio 1:15. By what angle road average climb? - Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube's s - Triangle

Calculate the area of the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius). - Square

Rectangular square has side lengths 183 and 244 meters. How many meters will measure the path that leads straight diagonally from one corner to the other? - Triangle

Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles. - Task

I have homework. The cube has an edge 7 cm long and I must find wall and body diagonal. - RT and circles

Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23. - Circle annulus

There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have? - Arc

Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m. - IS trapezoid

Isosceles trapezoid arm measured 35 cm. Height is 30 cm and middle segment is 65 cm. Determine length of its bases. - Tetrahedron

Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm. - Road embankment

Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters? - Base

Compute base of an isosceles triangle, with the arm a=20 cm and a height above the base h=10 cm. - Thales

Calculate the length of the Thales' circle described to right triangle with hypotenuse 44.2 cm. - Gon functions

Decide which of the numbers (values of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1. - Diagonal

Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm. - Arm

Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 14 cm and a height v=18 cm. - Block

Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9° - Maple

Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple. - Oil rig

Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes? - Diagonals

Rhombus has two diagonals e=14 dm and f=11 dm. Calculate the side angle and height of the rhombus. - Isosceles triangle

What are the angles of an isosceles triangle ABC if its base is long a=5 m and has an arm b=4 m. - Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees. - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone. - XY triangle

Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y. - Leg and height

Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m. - Pyramid

Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges. - Angles in a triangle

The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle? - Without Euclid laws

Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws. - Areaf of ST

It is given square DBLK with side |BL|=13. Calculate area of triangle DKU if vertex U lie on line LB. - Right angled

From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square? - Isosceles trapezoid

Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid. - Rhombus

Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 84 dm and the other diagonal BD has length 20 dm. - Railway

Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent? - Prism

Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 47 cm and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5. - 7 triangle

The triangle area is 26.7 cm^{2}. Determine the side length l if appropriate height h_{l}= 45.3 cm. - Unit vector 2D

Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10]. - Column

Perpendicular pole high 8 m tall broke and its toe fell 2.7 m from the bottom of the pole. At what height above the ground pole broke? - Rectangle

Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Map - climb

On the map of High Tatras in scale 1:11000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 354.6 mm. Altitude of this stations are 949 m and 1760 m. What is average angle of climb of this cable car track? - Center of the cube

Center of the cube has distance 16 cm from each vertex. Calculate the volume V and surface area S of the cube. - Triangle radians

The size of two internal angles of a triangle ABC are α=6/18π and β=7/18π. Calculate the size of the third angle. - Space diagonal

The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube. - Horizon

The top of a lighthouse is 19 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.] - OPT

What is the perimeter of a right triangle with the legs 14 cm and 21 cm long? - Right triangle

Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard? - Train

The train is running at speeds of 96 km/h. From the beginning of braking to full stop train run for 3.3 minutes. If the train slows the braking equally, calculate the distance of the place from the station where you need to start to brake. - Shooter

The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot? - Hexagon A

Calculate area of regular hexagon inscribed in circle with radius r=9 cm. - RT 10

Area of right triangle is 84 cm^{2}and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees. - Trapezoid ABCD

Calculate the perimeter of trapezoid ABCD if we know the side c=15, b=19 which is also a height and side d=20. - Cable car 2

Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car? - House roof

The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m^{2}is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof? - Tower

The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m^{2}of the sheet is required to cover the top of the tower if we count 8% of the sheet waste? - The bridge

Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle? - Inscribed rectangle

The circle area is 216. Determine the area of inscribed rectangle with one side 5 long. - Chord - TS

The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS? - Flowerbed

Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex? - Trapezoid ABCD v2

Trapezoid ABCD has length of bases in ratio 3:10. The area of riangle ACD is 825 dm^{2}. What is the area of trapezoid ABCD? - Isosceles IV

In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle. - Chord - TS v2

The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS? - 30-60-90

The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg? - ISO trapezium

Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees. - Leg

Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg. - Distance

Wha is the distance between the origin and the point (18; 22)? - Vector sum

The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v? - Diamond

Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area. - Box

Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top. How many cm^{2}of cardboard we need to cover overlap and joints that are 5% of are - Triangle

The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of this triangle. - Ladder

8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder? - RT 11

Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long. - KLMN

In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN. - Park

In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m. - Sails

We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail? - Euclidean distance

Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD. - Quadrilateral

In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm^{2}, what is the area of ABCD? - Cone and the ratio

Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface. - Cosine

The point (8, 6) is on the terminal side of angle θ. cos θ = ? - Catheti

The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs. - Hexagon 5

The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon. - Climb

For horizontal distance 4.2 km road rise by 6.3 m. Calculate the road pitch in ‰ (permille, parts per thousand). - Pentagonal pyramid

Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees. - Rhumbline

Find circumference and area of the rhumbline ABCD if the short side AD of which has a length of 5 cm, and the heel of the height from D leading to the AB side divides the AB side into two sections of 3 cm and 4 cm. - Triangular prism

Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism. - Sphere and cone

Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone? - Climb in percentage

The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km. - Sphere - parts

Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm. - ISO trapezoid v2

bases of Isosceles trapezoid measured 16 cm and 4 cm and its perimeter is 47 cm. What is the are of a trapezoid? - Triangular prism

The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism. - ISO Triangle V2

Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle. - Tree

How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground. - Cathethus and the inscribed circle

In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle. - Obtuse angle

The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image) - Parallelogram ABCD

The area of parallelogram ABCD is 440 cm^{2}. Points M and N are the midpoints of the sides AB and BC. What is the area of a quadrilateral MBND? - Railway

Between points A, B, whose horizontal distance is 1.5 km railway line has 8promile climb. Between points B, C with horizontal distance of 900 m is climb 14promile. Calculate differences of altitudes between points A and C. - Goat and circles

What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g - Spherical cap

What is the surface area of a spherical cap, the base diameter 20 m, height 2 m. - ISO triangle

Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm. - Trapezoid - diagonal

Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm^{2}. What is the area of the trapezoid? - Triangular pyramid

It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm^{3}. What is it content (surface area)? - Isosceles trapezoid

Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm. - Triangle

Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17. - Right angled triangle

Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs. - Circles

In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both). - RT and ratio

A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs? - Goat

Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow? - Median

In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb. - Hexa pyramid

The base of the regular pyramid is a hexagon, which can be described by a circle with a radius of 1 m. Find the volume of the pyramid 2.5 m high. - Bevel

I have bevel in the ratio 1:6. What is the angle and how do I calculate it? - Angles and sides of the triangle

Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ? - Same area

There is a given triangle. Construct a square of the same area. - The diagram 2

The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm^{2}. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone - Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long. - Again saw

From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 146 mm and 128 mm. What is the trunk smallest diameter? - Concentric circles

In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord. - Triangle midpoints

Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC. - Trapezoid - hard example

Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter. - Medians and sides

Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6). - 3d vector component

The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3? - Ladder 2

Ladder 6.4 meters long is positioned in the well such that its lower end is distanced from the wall of the well 1.2 m. The upper part of the ladder is supported on the upper edge of the well. How high is the well? - Isosceles trapezoid

The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid. - Medians in triangle

Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm. - Angles of the triangle

ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC. - Angles in ratio

The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z. - Tent

Pyramid-shaped tent has a base square with a side length of 2 m and a height 1.7 m. How many meters of canvas is nneded to make it if for a waste should be added 10%? - The chord

Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°? - Internal angles

One internal angle of the triangle JAR is 25 degrees. The difference is the size of the two other is 15°. Identify the size of these angles. - Angles ratio

In a triangle ABC true relationship c is less than b and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is: - Triangle angles

In a triangle ABC the interior angle at the vertex C is twice as the internal angle at the point A. Outer angle at the point B measured 117 degrees. How big is the outer angle at the vertex A? - Rhomboid

The dimensions of the rhomboid sides are a= 5cm, b = 6 cm and the size of the angle at the vertex A is 60°. What is the length of side AC? - Cardboard box

We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we ca - Circular sector

I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector? - Diamond

Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal. - The farmer

The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th - Regular quadrangular pyramid

How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%. - Chord 2

Point A has distance 13 cm from the center of the circle with radius r = 5 cm. Calculate the length of the chord connecting the points T1 and T2 of contact of tangents led from point A to the circle. - Rectangular trapezoid

Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC. - Right triangle

Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC. - High wall

I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall? - Pyramid - angle

Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees. - Perimeter and legs

Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm^{2}. - Flowerbed

Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m^{2}= - Field with vegetables

Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated? - Right trapezoid

The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length 0.25 dm. Calculate the lengths of the diagonals and the second leg. - Parcel

parcel has a rectangular shape of a trapezoid with bases 12 m and 10 m and a height 8 m. On parcel was built object with a footprint an isosceles triangle shape with side 4 m and height three-quarters of a meter. What is the area of unbuild parcel? - Trapezoid RT

The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumpti - Road - permille

5 km long road begins at an altitude 500 meters above sea level and ends at a altitude 521 ASL. How many permille road rises? - The fence

I'm building a fence. Late is rounded up in semicircle. The tops of late in the field between the columns are to copy an imaginary circle. The tip of the first and last lath in the field is a circle whose radius is unknown. The length of the circle chord - Nine-gon

Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm. - Circle inscribed

Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm. - Inscribed triangle

To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle. - Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u_{1}= 12 cm and u_{2}= 10 cm. Prism height is twice base edge length. - Clock face

clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles. - RTriangle 17

The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs. - Euclid 5

Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height v_{c}= 5 cm. - Chord AB

What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm? - Bearing - navigation

A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer. - Chord 4

I need to calculate the circumference of a circle, I know the chord length c=22 cm and the distance from the center d=29 cm chord to the circle. - Find the area

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft - Scalene triangle

Solve the triangle: A = 50°, b = 13, c = 6 - Triangle

Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201 - Two forces

Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer. - Airplane navigation

An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)? - Triangle SSA

Construct a triangle ABC if |AB| = 5cm v_{a}= 3cm, CAB = 50 °. It is to create the analysis and construction steps. - Right triangle ABC

Calculate the perimeter and area of a right triangle ABC, if you know the length of legs 4 cm 5.5 cm and 6.8 cm is hypotenuse. - Triangular prism

Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm. - Draw a trapezoid

Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task. - Internal and external angles

Calculate the remaining internal and external angles of a triangle, if you know the internal angle γ (gamma) = 34 degrees and one external angle is 78 degrees and 40 '. Determine what kind of triangle it is from the size of its angles. - Angles in triangle

Calculate the alpha angle in the triangle if beta is 61 degrees and 98 gamma degrees. - Hexagonal pyramid

Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high. - The cone

The lateral surface area of the cone is 4 cm^{2}, the area of the base of the cone is 2 cm^{2}. Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base c - Chimney

Lower circumference of of the chimney is 12.57 m, top circumference is 5.655 m. The slope of the walls is 87°. Determine the height of the chimney. - RT leg and perimeter

Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269. - Triangle IRT

In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB. - Triangular pyramid

Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm - Arm-leg

Calculate the length of the base of an isosceles triangle with a circumference 224 cm if the arm length is 68 cm. - 4side pyramid

Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees. - Pyramid

Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC. - 3sides prism

The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism. - Circular pool

The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool? - Church tower

Archdeacon church in Usti nad Labem has diverted tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Result write in degree's minutes. - Lift

The largest angle at which the lift rises is 16°31'. Give climb angle in permille. - Ballistic curve

The ballistic grenade was fired at a 45° angle. The first half ascended, the second fall. How far and how far it reached if his average speed was 1200km/h, and 12s took from the shot to impact. - Triangle ABC

In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC. - Carpet

The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diago - Construct 1

Construct a triangle ABC, a = 7 cm, b = 9 cm with right angle at C, construct the axis of all three sides. Measure the length of side c (and write). - Pine wood

From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lu - Diamond ABCD

In the diamond ABCD is the diagonal e = 24 cm and size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond. - Alfa, beta, gama

In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC. - Forces

Determine the resultant of two perpendicular forces F_{1}= 560 N and second force of 25% smaller. - Journey

Charles and Eva stands in front of his house, Charles went to school south at speed 5.4 km/h, Eva went to the store on a bicycle eastwards at speed 21.6 km/h. How far apart they are after 10 minutes? - Cableway

Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station. - Broken tree

The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak? - Rhombus IV

Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm. - Diagonals in diamond

In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals. - Drainage channel

The cross section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m, 0.90 m and arm has length 0.60 meters. Calculate the depth of the channel. - Length IT

Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm - Dusan

a) Dusan break two same window, which has triangular shape with a length of 0.8 m and corresponding height 9.5 dm. Find how many dm^{2}of glass he needs to buy for glazing of these windows. b) Since the money to fix Dusan has not, must go to the paint job - Triangle ABC

Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled? - Katy MO

Kate draw triangle ABC. Middle of AB have mark as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occupy 4-gon AXZY? - Trio 2

Decide whether trio of numbers is the side of a right triangle: 26,24,10. - Hypotenuse

Calculate the length of the hypotenuse of a right triangle with a catheti 71 cm and 49 cm long. - Acreage

What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ? - Dog

Dog is tied to a chain, which is mounted in a corner of the yard. Yard has the shape of a square with a side length of 20 meters. The same long is also dogchain. Are there places in the yard where dog can't reach? - Park

In the park is marked diamond shaped line connecting locations A, D, S, C, B, A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m. - Triangular pyramid

Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm. - Chord circle

The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch. - Sides of the triangle

Calculate triangle sides where its area is S = 84 cm^{2}and a = x, b = x + 1, xc = x + 2 - Diagonal - simple

Calculate the length of the diagonal of a rectangle with dimensions 5 cm and 12 cm. - Right triangle - leg

Calculate to the nearest tenth cm length of leg in right-angled triangle with hypotenuse length 9 cm and 7 cm long leg. - Triangle - is RT?

Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, side c is 31 cm longer than side a. Calculate the length of sides and determine whether triangle is a right triangle. - Mountain railway

Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track. - Tetrahedral pyramid

Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm^{2}and deviation angle of the side edges from the plane of the base is 60 degrees. - Central park in city

The city park has the shape of a rectangle of 180 meters in length and 120 meters in width. People make their walk through the center of the park from one corner to the second. Calculate how many meters this way is shorter than they walked along the path - Ladder

The ladder has a length 3.5 meters. He is leaning against the wall so that his bottom end is 2 meters away from the wall. Determine the height of the ladder. - The double ladder

The double ladder has 3 meters long shoulders. What is the height of the upper of the ladder reach if the lower ends are 1.8 meters apart? - Four ropes

TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment - Stairway

Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm. - Ethernet cable

Charles and George are passionate gamers and live in houses that are exactly opposite each other across the street, so they can see each other through the windows. They decided that their computers will connect the telephone cable in order to play games t - Dig water well

Mr. Zeman digging a well. Its diameter is 120 cm, and plans to 3.5 meters deep. How long (at least) must be a ladder, after which Mr. Zeman would have eventually come out? - Isosceles trapezoid

Calculate the circumference and the contents of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm and the size of the arms is 5 cm. - Is right?

Determine whether the triangle with legs (catheti) 19.5 cm and 26 cm and length of the hypotenuse 32.5 cm is rectangular? - Two aircraft

Two planes fly to the airport. At some point, the first airplane is away from the airport 98 km and the second 138 km. The first aircraft flies at an average speed of 420 km/h, the second average speed is 360 km/h, while the tracks of both planes are perp - 3s prism

It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism. - Medians of isosceles triangle

The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians? - Pyramid 8

Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°. - Quadrilateral prism

Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°. - Tree trunk

From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section. - Points on circle

In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are - Cube - wall

V kocke ABCDEFGH je ?. Aký je povrch kocky? - Windbreak

A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree? - Embankment

Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long. - Circle chord

Calculate the length of the chord of the circle with radius r = 10 cm, length of which is equal to the distance from the center of the circle. - Kite

John a kite, which is diamond shaped. Its diagonals are 60 cm long and 90 cm long. Calculate: a) the diamond side b) how much paper John needs to make a kite if he needs paper on both sides and needs 5% of the paper for bending. - Hexagon area

The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area. - Road drop

On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane? - Outer contact of circles

Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contact. Calculate the perimeter of the triangle S_{1}S_{2}S_{3}. - Inscribed circle

Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1]. - Complete construction

Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs. - 6 regular polygon

It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm^{2}(square centimeters) has a circle in which is inscribed the 6-gon. - Steps

Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º and the length of the step is 28.6 cm. Report the result in centimeters to the nearest centimeter. - The ditch

Ditch with a cross-section of an isosceles trapezoid with bases 2m and 6m are deep 1.5m. How long is the slope of the ditch? - Diamond side

The diagonals of the diamond are 18 cm and 14 cm long. Calculate the length of the diamond side. - Diagonals in diamons/rhombus

Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal. - Two balls

Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them. - Vertical prism

The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism - Hexa prism

Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm. - Decagon prism

A regular decagon of side a = 2 cm is the base of the perpendicular prism, the side walls are squares. Find the prism volume in cm^{3}, round to two decimal places. - Perimeter of circle

Calculate the circumference of described circle to the triangle with sides 9,12,15 cm. - Trapezium ABCD

In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60 - Triangular prism

Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume. - Prism

The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters? - Is right triangle

One angle of the triangle is 36° and the remaining two are in the ratio 3:5. Determine whether triangle is a rectangular triangle. - Angles of a triangle

In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle. - Octagonal mat

Octagonal mat formed from a square plate with a side of 40 cm so that every corner cut the isosceles triangle with leg 3.6 cm. What is the content area of one mat? - Lamp cone

Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm. - Clouds

From two points A and B on the horizontal plane was observed forehead cloud above the two points under elevation angle 73°20' and 64°40'. Points A , B are separated by 2830 m. How high is the cloud? - Cone container

Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package. - Rectangular trapezium

Calculate the perimeter of a rectangular trapezium when its content area is 576 cm^{2}and sice a (base) is 30 cm, height 24 cm. - Smallest internal angle

Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8 - Inscribed circle

XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm. - Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm. - Segment in a triangle

In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB. - Centre of mass

The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p. - Concrete block

Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters. - Body diagonal

Find the cube surface if its body diagonal has a size of 6 cm. - Prism - box

The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm^{3}. Calculate the surface of the prism. - Circumscribed circle to square

Find the length of a circle circumscribing a square of side 10 cm. Compare it to the perimeter of this square. - Roof of the church

The cone roof of the church has a diameter of 3m and a height of 4m. What is the size of the side edge of the church roof (s) and how much sheet will be needed to cover the church roof? - Circular ring

Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form. - Cuboid - volume, diagonals

The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid? - Cube

Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm^{2}. - Flowerbed

Family cultivated tulips on a square flower bed of 6 meters. Later they added the square terrace with a side of 7 meters to their house. One vertex of the terrace lay exactly in the middle of a tulip bed, and one side of the terrace divided the side of th - Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface. - Regular triangular prism

Calculate the surface area of body of regular triangular prism, when the length of its base edge is 6.5 cm and height 0.2 m. - Hexagonal pyramid

Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid. - Cone

The rotating cone volume is 9.42 cm^{3}, with a height 10 cm. What angle is between the side of the cone and its base? - Pyramid

The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid. - Cube diagonals

Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm. - Rotating cone

Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm. - Support colum

Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m. - Pyramid 4sides

Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm. - Four sides of trapezoid

Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area. - Wall height

Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm. - RT perimeter

The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference. - Pyramid four sides

In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters. - Rotary bodies

The rotating cone and the rotary cylinder have the same volume 180 cm^{3}and the same height v = 15 cm. Which of these two bodies has a larger surface area? - The tent

The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m^{2}of cloth we need to make the tent if we have to add 7% of the seams? How many m^{3}of air will be in the tent? - Pyramid in cube

In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid. - Sphere equation

Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Hexagonal prism 2

The regular hexagonal prism has a surface of 140 cm^{2}and height of 5 cm. Calculate its volume. - Cone

Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long. - Church roof

The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required? - Triangular prism

The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm^{2}and the body height is 10 cm. Calculate the body volume. - Circle tangent

It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p. - A mast

A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken? - Rectangular triangle PQR

In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal - Hypotenuse

Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters. - Broken tree

The tree is broken at 4 meters above the ground and the top of the tree touches the ground at a distance of 5 from the trunk. Calculate the original height of the tree. - Internal angles

Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at the vertex A. - Tetrahedral pyramid

It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges. - Horizontal Cylindrical Segment

How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank? - Sides of triangle

Triangle has circumference 42 cm. Side a is 2 times shorter than side b and sice c is 2 cm longer than side a. Determine the sizes of sides of a triangle. - The field

The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters. - Alfa beta gama

The triangle's an interior angle beta is 10 degrees greater than the angle alpha and gamma angle is three times larger than the beta. Determine the size of the interior angles. - Triangle ABC

Construct a triangle ABC is is given c = 60mm hc = 40 mm and b = 48 mm analysis procedure steps construction - Trapezoid

trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area? - Minute

Two boys started from one place. First went north at velocity 3 m/s and the second to the east with velocity 4 m/s. How far apart they are after minute? - Right triangle

It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b - Hexagon rotation

A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated? - Regular quadrilateral pyramid

Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm. - Diagonals

A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal. - Cablecar

Funicular on Petrin (Prague) was 408 meters long and overcomes the difference 106 meters in altitude. Calculate the angle of climb. - Billiard balls

A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. - Glass

How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm? - Angle

Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence. - Bearing

A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point. - Plane II

A plane flew 50 km on a bearing 63degrees20 and the flew on a bearing 153degrees20 for 140km. Find the distance between the starting point and the ending point - Forces

Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant? - Three vectors

The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces. - Moon

We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth. - Hot air balloon

The center of the balloon is at an altitude of 600 m above the ground (AGL). From habitat on earth is the center of the balloon to see in elevation angle 38°20' and the balloon is seen from the perspective of angle 1°16'. Calculate the diameter of the bal - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - Cuboid easy

The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid. - Chocolate roll

The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this - Diagonals

Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus. - Resultant force

Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25° - Two diagonals

The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal? - Ladder

Ladder 10 meters long is staying against the wall so that its bottom edge is 6 meters away from the wall. What height reaches ladder? - Two cyclists

Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start? - Trapezoid MO-5-Z8

ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm^{2}. Determine the area of the trapezoid - Isosceles - isosceles

It is given a triangle ABC with sides /AB/ = 3 cm /BC/ = 10 cm, and the angle ABC = 120°. Draw all points X such that true that BCX triangle is an isosceles and triangle ABX is isosceles with the base AB. - Medians and sides

Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides. - Rhombus and diagonals

The a rhombus area is 150 cm^{2}and the ratio of the diagonals is 3:4. Calculate the length of its height. - Cube and sphere

Cube with the surface area 150 cm^{2}is described sphere. What is sphere surface? - Right triangle eq2

Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle. - Regular n-gon

Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm? - Rectangle 3-4-5

The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle. - 2d shape

Calculate the content of a shape in which an arbitrary point is not more than 3 cm from the segment AB. The length of the segment AB is 5 cm. - Pentagon

Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm. - Triangle ABC v2

Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x. - Midpoints

Triangle ABC with sides a = 5 cm, b = 3 cm, c = 40mm has a midpoint of K, L, M. How many centimeters is long perimeter of parallelogram KBLM? - Four sided prism

Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane. - Ratio iso triangle

The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure. - The rope

A 68 centimetre long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimetres what is the distance between the other two corners? - Rectangular trapezoid

The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid. - Rhombus

One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus. - How far

From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse? - Ladder

4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Triangle ABC

In a triangle ABC side b measure 10 cm less than the side a and side b is half of the side c. Calculate the length of sides if the circumference of the triangle is 42 cm. - Diagonals of diamond

Find the area and circumference of the diamond ABCD with 15m and 11m diagonals. - Two aircraft

From the airport will start simultaneously two planes, which fly tracks are perpendicular to each other. The first flying speed of 680 km/h and the second 840 km/h. Calculate how far the aircraft will fly for half an hour. - Square

Calculate the perimeter and the area of square with a diagonal length 30 cm. - Land - isosceles trapezoid

Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m. - Isosceles triangle

Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm. - Billboard

Rectangular billboard is 2.5 m long with a diagonal 2.8 m long. Calculate the perimeter and the content area of the billboard. - Double ladder

The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart? - Calculate

Calculate the area of the ABE triangle AB = 38mm and height E = 42mm ps: please try a quick calculation - Diagonals

Draw a square ABCD whose diagonals have a length of 6 cm - Isosceles right triangle

Contents of an isosceles right triangle is 18 dm^{2}. Calculate the length of its base. - Trapezoid thirds

The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment. - Circular segment

Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ) - Cube in sphere

The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere. - Trapezoid MO-5-Z8

Trapezoid KLMN has bases 12 and 4 cm long. The area of triangle KMN is 9 cm^{2}. What is the area of the trapezoid KLMN? - Center of gravity

In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. - Angles ratio

The internal angles of a triangle are in ratio 1:4:5 What kind of triangle is it? (solve internal angles and write down and discuss) - 30-gon

At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area. - Compute 4

Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long. - Forces on earth directions

A force of 60 N [North] and 80 N [East] is exerted on an object wigth 10 kg. What is the acceleration of the object? - Right triangle trigonometrics

Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent) - Tree

Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree? - Four sides of trapezoid

In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles. - Angles by cosine law

Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem). - Vertices of RT

Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle. - Triangular prism

Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides 6 cm 8 cm and 8 cm - Acceleration 2

if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem - Isosceles trapezoid

What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm? - Square circles

Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm. - Parallelogram +ľ

| AB | = 76cm, | BC | = 44cm, angle BAD = 30 °. Find the area of the parallelogram. - Nice prism

Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Juice box

The juice box has a volume of 200ml with its base is an isosceles triangle with sides a = 4,5cm and a height of 3,4cm. How tall is the box? - Children pool

The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm. A) How many liters of water can fit into the pool? B) The pool is made of a double layer of plastic film - Angle of deviation

The surface of the rotating cone is 30 cm^{2}(with circle base), its surface area is 20 cm^{2}. Calculate the deviation of the side of this cone from the plane of the base. - Satin

Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin? - Square pyramid

Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees. - Triangular prism

Calculate the volume and surface of the triangular prism ABCDEF with base of a isosceles triangle. Base's height is 16 cm, leg 10 cm, base height vc = 6 cm. The prism height is 9 cm. - Square

Danov's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg? - Circle and rectangle

A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle. - Roof 7

The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate? - Rectangle 35

Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length. - Vector 7

Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|. - Trapezoid - RR

Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm - Inner angles

The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places. - Water channel

The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flo - Tree shadow 3

A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m ? - Isosceles trapezoid

Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high. - Truncated cone 5

The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone? - Rhombus MATH

Construct a rhombus M A T H with diagonal MT=4cm, angle MAT=120° - Angles

In the triangle ABC, the ratio of angles is: a:b = 4: 5. The angle c is 36°. How big are the angles a, b? - Laths

There are two laths in the garage opposite one another: one 2 meters long and the other 3 meters long. They fall against each other and lean against the opposite walls of the garage both laths and touch at a height of 70 cm above the garage floor. How wid - Cube wall

Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume. - Isosceles triangle

The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area. - Largest angle of the triangle

What is the largest angle of the triangle if the second angle is 10° greater than twice the first and the third is 30° smaller than the second? - Perimeter of triangle

In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference. - Outer angles

The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertx B is 136°50'. What size has the inner triangle angle at the vertex C? - Diagonal 20

Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be? - Triangle KLM

In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm - Triangular prism

Calculate the volume and surface area of a triangular prism if it is given: a = 6.8 dm. ..Va = 4 dm. (base edge length and base triangle height length) ... ... .v = 23 dm (body height) - ABCD

AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - Cube wall

The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube. - The mast

A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - Body diagonal

Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base, - Right angled triangle 2

LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n - Is right triangle

Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m - Quadrangular prism

Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm. - Ladder slope

What is the slope of a ladder 6.2 m long and 5.12 m in height. - Trapezium internal angles

A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D. - Surface area of the top

A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder. - Chord

It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB. - Inscribed circle

The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c. - Parallelogram perimeter

The ABC triangle with sides a = 5cm, b = 3cm, c = 40mm has the center of the sides of the K,L,M. How many cm have the KBLM parallelogram perimeter? - Cylinder horizontally

The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder? - Tangent 3

In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm. - Two diagonals

The diagonals of the diamond EFGH have lengths in the ratio 1: 2. What is the circumference of a rhombus if the longer of the diagonals is 8 cm long? - Tangent

What distance is the tangent t of the circle (S, 4 cm) and the chord of this circle, which is 6 cm long and parallel to the tangent t? - Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =? - Conical area

A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation. - Sides of triangle

Triangle circumference with two identical sides is 117cm. The third side measures 44cm. How many cms do you measure one of the same sides? - Clouds

Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us? - The pole

The telegraph pole is supported by a 4 m bullet at 3/4 of its height, the end of which is at a distance 2.5 m from the pole post. Calculate the height of the telegraph pole. - Garden fence

The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced? - Pendulum

Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm. - Equation of circle 2

Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x. - Diagonal

he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal. - Tetrahedron

What is the angle of the sides from the base of a three-sided pyramid where the sides are identical? - Right-angled triangle

Determine the content of a right triangle whose side lengths form successive members of an arithmetic progression and the radius of the circle described by the triangle is 5 cm. - Tv screen

The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen? - Two forces

The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F. - Body diagonal

Calculate the length of the body diagonal of the 6cm cube. - Bamboo

Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken? - ABCD square

In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Inscribed circle

Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC. - Sum of squares

The sum of squares above the sides of the rectangular triangle is 900 cm^{2}. Calculate content of square over the triangle's hypotenuse. - Construct

Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long. - Coordinate axes

Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y. - Right triangular prism

We have cuboid with a base and dimensions of 12 cm and 5 cm and height of 4 cm. The tablecloth cut it into two identical triangular prisms with right triangular bases. The surface of the created prisms was painted with color. Calculate the surface area of - Ruler and compass

Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°. - Complementary angles 2

Two complementary angles are (x+4) and (2x - 7) find the value of x - Three points 2

The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D. - Painters

Six of the painters paint 90 m of fence in five hours. For how long would the 4 painters paint a 45 meter fence? How many meters fence painted painters 5 for two hours? - Diagonal to area

Calculate the area of a rectangle in which the length of the diagonal is 10 cm. - Rhombus 29

One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus. - A bridge

A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. - Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - Body diagonal - cube

Calculate the surface and cube volume with body diagonal 15 cm long. - Cube cut

The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '. - Ratio of sides

The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm. - Roof cover

Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m^{2}of sheet metal is needed to cover this roof if 5.5% of the sheet we must add for joints and waste. - Right angled triangle 3

Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length. - Diamond diagonals

Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm. - Regular quadrangular pyramid

The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes? - Hexagon ABCDEF

In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area. - A cylinder

A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm? - Thunderstorm

The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tria - Hypotenuse - RT

A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle? - A box

A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R? - Quadrangular pyramid

Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area. - Find radius

Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r - Thomas

Thomas lives 400 meters away from Samko, Robo from Thomas also 400 m and Samko from Robo 500. Anton lives 300 meters away from Robo further as Samko. How far away lives Anton from Rob? - The Scout Tent

The Scout Tent has a rectangular wooden underlay with dimensions of 220 cm and 150 cm. How much canvas is needed for a 170 cm high of pyramid roof? - A triangle

A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles? - Square

Square JKLM has sides of length 24 cm. Point S is the center of LM. Calculate the area of the quadrant JKSM in cm^{2}. - Area of a triangle

What is the area of a triangle that has the base 4 1/4 and the height of 3 3/3? - Rhombus

The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height - Solid cuboid

A solid cuboid has a volume of 40 cm^{3}. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Find the 3

Find the distance and mid-point between A(1,2) and B(5,5). - Triangular prism

Calculate the surface of a regular triangular prism with a bottom edge 8 of a length of 5 meters and an appropriate height of 60 meters and prism height is 1 whole 4 meters. - Ratio of edges

The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - Ditch

Ditch profile is an isosceles trapezoid with bases of length 80m and 60m. The slope of the side wall of the ditch is 80°. Calculate the ditch depth. - Six-sided polygon

In a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle. - In a 2

In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. . - If the

If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. . - Ellipse

Ellipse is expressed by equation 9x^{2}+ 25y^{2}- 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse. - Hyperbola

Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6]. - Lampshade

The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm^{2}of material will we need when we 10% is waste? - Angle of diagonal

Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume. - Two heights and a side

Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm and height to side b: vb = 4 cm. - Christmas napkins

The girls embroidered Christmas napkins. Each napkin had the shape of a triangle with sides of 5 dm, 60 cm, and 800 mm. How many cms did the girls sew if they made 15 napkins? - Prove

Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Right triangle

Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'. - Double ladder

The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach? - Three sides

Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. . - Two chords

There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure. - Isosceles

Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area. - Is right-angled

Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 and √8) be a right triangle? - Paper box

Calculate how much we'll pay for a three-side shaped prism box with a triangular base, and if it measures 12cm and 1.6dm, the hypotenuse measures 200mm. The box is 34cm high. We pay 0,13 € per square meter of paper. - Cone 15

The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height? - Right triangle from axes

A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment? - Two people

Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa - Find the 5

Find the equation of the circle with center at (1,20), which touches the line 8x+5y-19=0 - A truck

A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)? - Sphere from tree points

Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - The pond

We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond? - SSA and geometry

The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer. - Isosceles triangle

The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z. - Decagon

Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m - Inscribed rectangle

What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long? Answer: 14 dm - Deviation of the lines

Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm - Distance of lines

Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm - Slant height

The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone - Is right triangle or not

If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area. - Depth angle

From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff? - Perpendicular prism

Calculate the volume of the perpendicular prism if its height is 60.8 cm and the base is a rectangular triangle with 40.4 cm and 43 cm legs. - Isosceles triangle

The circumference of the isosceles triangle is 32.5 dm. Base length is 153 cm. How long is the leg of this triangle? - Cross road

From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes? - Bricklayer

How much do we pay for a bricklayer laying a pavement in a square room with a diagonal of 8 m, if 1 sqm with work will cost for CZK 420? - Quarter circle

What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Paratrooper

After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity with respect to the ground, b) the distance of his land fr - The swimmer

The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion - Pavement

Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m. - Sss triangle

Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm - Diagonals of pentagon

Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm. - MO Z8–I–6 2018

In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line. - AP RT triangle

The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area? - Diagonals of a rhombus 2

One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm^{2}, find the side of the rhombus. - Square

Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm^{2}? - Cube diagonals

The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - Distance problem

A=(x, x) B=(1,4) Distance AB=√5, find x; - Distance problem 2

A=(x,2x) B=(2x,1) Distance AB=√2, find value of x - Construct

Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description. - Center of line segment

Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is . - On line

On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0]. - Three points

Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k? - The mast

The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole? - The garden

The garden has the shape of a rectangular trapezium. The bases have lengths of 27 meters and 36 meters, the trapezoid's height is 12 meters. Calculate how much fence will cost this garden if one meter costs 1.5 €? - Right 24

Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you. - Right isosceles triangle

Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle? - Rectangular garden

The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden. - Ladder

Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder? - RT - inscribed circle

In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle. - Body diagonal

Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal. - Elevation angles

From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain? - Isosceles trapezium

Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm. - Diagonals of the rhombus

How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm^{2}? - Spruce height

How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree? - Isosceles trapezoid

The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros? - Pilot

How high is the airplane's pilot to see 0.001 of Earth's surface? - Waste

How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area? - Calculate 2

Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm - Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm^{2}and side is 13 cm long. - Cube diagonals

Calculate the length of the side and the diagonals of the cube with a volume of 27 cm^{3}. - Find diagonal

Find diagonal of cuboid with length=20m width=25m height=150m - Land

Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land? - KLMN trapezoid

The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K? - Octagonal tank

The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness. - Axial cut of a rectangle

Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long. - Circle described

The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle. - One trapezium

One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area. - Cuboidal room

Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room - Vertices of a right triangle

Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle. - Triangle perimeter

Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long. - Angle at the apex

In an isosceles triangle, the angle at the apex is 30° greater than the angle at the base. How big are the internal angles? - Cube cut

In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane. - Quadrangular pyramid

The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area. - Regular triangular pyramid

Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters - Children playground

The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles. - Tetrahedral pyramid

Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m. - Rectangular field

A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field. - Tangent spheres

A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and - Rectangular triangle

The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle? - Isosceles triangle

In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm? - An angle

An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x. - Balloon and bridge

From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge. - KLM triangle

Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees. - Two parallel chords

The two parallel chords of the circle have the same length of 6 cm and are 8 cm apart. Calculate the radius of the circle. - Triangular pyramid

What is the volume of a regular triangular pyramid with a side 3 cm long? - Rectangle

There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle. - Prism diagonal

The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism? - Triangle 42

Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=? - Spherical cap

Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm^{2}. Determine the radius r of the sphere from which the spherical cap was cut. - Cincinnati

A map is placed on a coordinate grid. Cincinnati located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? Round to the nearest tenth. - Pile of sand

A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand. - Horizontal distance

The road has a gradient of 8%. How many meters will the road rise on a horizontal distance of 400m? - Spherical cap 4

What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. - Cable car

Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m. - Isosceles triangle 8

If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree. - Find the 9

Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3 - Find parameters

Find parameters of the circle in the plane - coordinates of center and radius: ? - The sides 2

The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid. - Cone side

Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side. - Medians 2:1

Median to side b (tb) in triangle ABC is 12 cm long. a. What is the distance of the center of gravity T from the vertex B? b, Find the distance between T and the side b. - Pyramid height

Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm. - Castle tower

The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap. - Prism 4 sides

The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters - Diamond and diagonals

A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!) - Triangular prism

Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm. - Perimeter of RT

Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm^{2}. - Height of the room

Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room? - RT sides

Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm. - Rectangular trapezoid

In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v. - A kite

ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD. - Lateral surface area

The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm. - Annular area

The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area. - Ratio of sides

Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7. - Angle of two lines

There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - One side

One side is 36 long with a 15° incline. What is the height at the end of that side? - Isosceles triangle 9

Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle - Three altitudes

A triangle with altitudes 4; 5 and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle. - Area of a rectangle

Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem. - The second

The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles? - Touch x-axis

Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - Base of prism

The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm^{2}. - Chauncey

Chauncey is building a storage bench for his son’s playroom. The storage bench will fit into the corner and against two walls to form a triangle. Chanuncy wants to buy a triangular shaped cover for the bench. If the storage bench is 2 1/2 ft. Along one wa - The triangle

The triangle is given by three vertices: A [0.0] B [-4.2] C [-6.0] Calculate V (intersection of heights), T (center of gravity), O - center of a circle circumscribed - Depth angles

At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad - Company logo

The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo? - The cable car

The cable car has a length of 3,5 kilometers and an angle of climb of 30 degrees. What is the altitude difference between Upper and Lower Station? - The ladder

The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach? - The tractor

The tractor sows an average of 1.5 ha per hour. In how many hours does it sows a rectangular trapezoid field with the bases of 635m and 554m and a longer arm 207m? - The Eiffel Tower

The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height. - Angles of elevation

From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of - Tetrahedral pyramid

A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area). - Wall and body diagonals

Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m - Faces diagonals

If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2 - Medians in right triangle

It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides? - Hole's angles

I am trying to find an angle. The top of the hole is .625” and the bottom of the hole is .532”. The hole depth is .250” what is the angle of the hole (and what is the formula)? - Uphill garden

I have a garden uphill, increasing from 0 to 4.5 m for a length of 25 m, how much is the climb in percent? - Body diagonal

Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm - Cuboid face diagonals

The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid. - A concrete pedestal

A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal. - The hemisphere

The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees? - Isosceles triangle 10

In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles. - A rhombus

A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus. - Coordinates of square vertices

I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter. - The trapezium

The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium. - A rectangle 2

A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths. - Circular railway

The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C? - Land boundary

The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary? - Construct rhombus

Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm - Inscribed circle

A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base? - Two circles

Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles? - Draw triangle

Construct an isosceles triangle ABC, if AB = 7cm, the size of the angle ABC is 47°, arms | AC | = | BC |. Measure the size of the BC side in mm. - Median in right triangle

In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse). - Hexagon

Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm. - Mysterious area

The trapezoid ABCD is given. Calculate its area if the area of the DBC triangle is 27 cm^{2}. - The aspect ratio

The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle. - Hexagonal pyramid

Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture. - Possible lengths

Find the most possible lengths for the third side of a triangle with sides 20 and 18. - Tetrahedral pyramid

Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´. - Octagonal pyramid

Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°. - Parametric form

Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. .. - Regular hexagonal pyramid

Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture. - Bisectors

As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE. - The Indian tent

The Indian tent is cone-shaped. Its height is 3.5 m. The diameter of the base is 2.5 m. How much canvas is needed to make a tire? - Axial section of the cone

The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square. - A drone

A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was at a height of 300 m above the plane of ABC. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in - Angled cyclist turn

The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn? - Squares above sides

Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm^{2}. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc - The quadrilateral pyramid

The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area. - Wall height

Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm. - Rectangular base pyramid

Calculate an area of the shell of the pyramid with a rectangular base of 2.8 m and 1.4 m and height 2.5 meters. - Two chords

In a circle with radius r = 26 cm two parallel chords are drawn. One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. Calculate the distance of two chords. - Quadrilateral pyramid

In a regular quadrilateral pyramid, the side edge is e = 7 dm and the diagonal of the base is 50 cm. Calculate the pyramid shell area. - Hexagonal pyramid

Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. - The bus stop

The bus stop waiting room has the shape of a regular quadrilateral pyramid 4 m high with a 5 m base edge. Calculate how many m^{2}roofing is required to cover the three walls of the sheathing, taking into account 40% of the additional coverage. - Storm and roof

The roof on the building is a cone with a height of 3 meters and a radius equal to half the height of the roof. How many m^{2}of roof need to be repaired if 20% were damaged in a storm? - A cell tower

A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal? - Angle of cone

The cone has a base diameter of 1.5 m. The angle at the main apex of the axial section is 86°. Calculate the volume of the cone. - The spacecraft

The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered a - Altitude difference

What a climb in per mille of the hill long 4 km and the altitude difference is 6 meters? - Free space in the garden

The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large - Triangular prism,

The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm^{3}(l). - Power line pole

From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole. - Tetrahedral pyramid 8

Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p - Tropics and polar zones

What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33' - What percentage

What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km - Coordinates of a centroind

Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians). - Annulus

Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n. - Five-gon

Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm. - Angle of the body diagonals

Using vector dot product calculate the angle of the body diagonals of the cube. - Right angle

If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6 - Chord BC

A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]? - Triangular prism

The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism. - Decide 2

Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line - Horses playground

The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m^{2}, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows? - Medians in RT

The rectangular triangle ABC has a length of 10 cm and 24 cm. Points P, Q, R are the centers of the sides of this triangle. The perimeter of the PQR triangle is: - Two groves

Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’? - Height of the cuboid

Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid? - The angle of view

Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other. - Base of an isosceles triangle

Calculate the size of the base of an isosceles triangle, the height is 5 cm and the length of the arm is 6.5 cm. What is the perimeter of this triangle? - Black diamond run

Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet. - RT triangle and height

Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm. - Height to the base

The triangle area is 35 cm ^ 2. The size of the base is 10 cm. Find the length of height to the base. - Difference of legs

In a right triangle, the length of the hypotenuse is 65 m, and the difference of legs is 23 m. Calculate the perimeter of this triangle. - A kite

Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain? - Clock hands

Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours. - Embankment

The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m^{3}of soil is in the embankment? - Wall and body diagonals

The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals. - The rescue helicopter

The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site? - Spherical cap

The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut. - Cone roof

How many m^{2}of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays. - Annulus from triangle

Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm - The conical

The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it? - The angles ratio

The angles in the ABC triangle are in the ratio 1: 2: 3. find the sizes of the angles and determine what kind of a triangle it is. - The bases

The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid. - Flakes

A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips? - In a

In a triangle, the aspect ratio a: c is 3: 2 and a: b is 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides. - Concentric circles and chord

In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord? - The right triangle

The right triangle ABC has a leg a = 36 cm and an area S = 540 cm^{2}. Calculate the length of the leg b and the median t2 to side b. - Probability

How probable is a randomly selected three-digit number divisible by five or seven? - The angles

The angles in the triangle are in the ratio 12: 15: 9. Find the angles. - Interior angles

Calculate the interior angles of a triangle that are in the ratio 2: 3: 4. - Triangle from median

Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5. - Triangular prism

Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm. - Observation tower

From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower? - Side lengths

In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b. - Interior angles

In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles. - Quadrilateral pyramid

Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm. - Viewing angle

The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure? - The tent

Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m. - Two parallel chords

In a circle 70 cm in diameter, two parallel chords are drawn so that the center of the circle lies between the chords. Calculate the distance of these chords if one of them is 42 cm long and the second 56 cm. - Circle and square

An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD. - Height of pyramid

The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height? - Diamond area from diagonals

In the diamond ABCD is AB = 4 dm and the length of the diagonal is 6.4 dm long. What is the area of the diamond? - The cable car

The cable car is 2610 m long and rises at an angle of 35°. Calculate the height difference between the lower and upper station of the cable car. - Surface of pyramid

In a regular quadrilateral pyramid, the height of the sidewall is equal to the length of the edge of the base. The content of the sidewall is 32 cm^{2}. What is the surface of the pyramid? - Telegraph poles

The bases of two adjacent telegraph poles have a height difference of 10.5 m. How long do the wires connect the two poles if the slope is 39° 30´? - The ladder

The ladder touch on a wall at a height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall? - TV tower

Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°? - Isosceles triangle

Calculate the size of the interior angles and the length of the base of the isosceles triangle if the length of the arm is 17 cm and the height to the base is 12 cm. - The right triangle

In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles. - Fighter

A military fighter flies at an altitude of 10 km. From the ground position, it was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h. - Traffic sign

There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls). - Right triangle - ratio

The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle. - Sailing

Solve the following problem graphically. The fishing boat left the harbor early in the morning and set out to the north. After 12 km of sailing, she changed course and continued 9 km west. Then When she docked and reached the fishing grounds she launched - Triangle in a square

In a square ABCD with side a = 6 cm, point E is the center of side AB and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. - Right angle

In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle. - Regular hexagonal prism

Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long. - Two chords

From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords. - Inclined plane

1. How much work W we have to do to pull a body weighing 200 kg along an inclined plane with a length of 4 m to a total height of 1.5 m. 2. Find the force we need to exert to do this if we neglect frictional resistance. 3. Find the force we would need if - The tower

The observer sees the base of the tower 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands? - Trip with compass

During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip? - Coordinates

Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0 - Dodecagon

Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees. - Pentadecagon

Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places. - Which

Which of the following numbers most accurately area of a regular decagon with side s = 2 cm? (A) 9.51 cm^{2}(B) 20 cm^{2}(C) 30.78 cm^{2}(D) 31.84 cm^{2}(E) 32.90 cm^{2} - Hexagonal pyramid

Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm. - Chord of triangle

If the whole chord of the triangle is 14.4 cm long, how do you calculate the shorter and longer part? - Sailboat

The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck. - Powerplant chimney

From the window of the building at a height of 7.5 m, the top of the factory chimney can be seen at an altitude angle of 76° 30 ′. The base of the chimney can be seen from the same place at a depth angle of 5° 50 ′. How tall is the chimney? - Integer sides

A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - Calculate 6

Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1]. - Parallelogram

Find the perimeter of the parallelogram, where base a = 8 cm, height v = 3 cm, and angle alpha = 35° is the magnitude of the angle at vertex A. - Triangular prism

The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm^{3}? And the surface cm^{2}? - Perimeter and diagonal

The perimeter of the rectangle is 82 m, the length of its diagonal is 29 m. Find the dimensions of the rectangle. - Find the 13

Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4]. - Hexagonal pyramid

Find the area of a shell of the regular hexagonal pyramid, if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm. - The regular

The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume. - Quadrilateral pyramid

A regular quadrilateral pyramid has a volume of 24 dm^{3}and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid - Quadrilateral oblique prism

What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35 ´ and the edges a, b form an angle of 50.5°. - Height

The content of the triangle is 35 cm^{2}. The length of the base is 10 cm. Determine the length of the height on the base. - Calculate 7

Calculate the height of the trapezoid ABCD, where coordinates of vertices are: A[2, 1], B[8, 5], C[5, 5] and D[2, 3] - Diagonal BD

Find the length of the diagonal BD in a rectangular trapezoid ABCD with a right angle at vertex A when/AD / = 8,1 cm and the angle DBA is 42° - Quadrilateral pyramid

In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place. - Hexagonal pyramid

Calculate the volume and surface area of a regular hexagonal pyramid with a base edge a = 30 m and a side edge b = 50 m. - Quadrilateral pyramid,

A quadrilateral pyramid, which has a rectangular base with dimensions of 24 cm, 13 cm. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid - Sphere in cone

A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele - Quadrilateral pyramid

We have a regular quadrilateral pyramid with a base edge a = 10 cm and a height v = 7 cm. Calculate 1/base content 2/casing content 3/pyramid surface 4/volume of the pyramid - Truncated pyramid

The concrete pedestal in the shape of a regular quadrilateral truncated pyramid has a height of 12 cm, the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base. - Three points

Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out: (a) whether the triangle KLM is right b) calculate the length of the line to the k side c) write the coordinates of the vector LM d) write the directional form of the KM side e) write the d - Inscribed and described circle

Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm. - Find the

Find the content of a regular 12 sided polygon, if its side a = 12 cm. - Isosceles triangle

In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C. - Isosceles trapezoid

Find the area of an isosceles trapezoid, if the bases are 12 cm and 20 cm, the length of the arm is 16 cm - Body diagonal

Find the length of the body diagonal of a cuboid with lengths of 16 cm, 7 cm, and 4 cm. - Trapezoid - construction

Construct a trapezoid KLMN, where: k = 9 cm, l = 4 cm, m = 5 cm and angle α = 45° - Sphere parts, segment

A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. .What are the volume of the segment and the surface of the segment? - Right triangle

A right triangle ABC is given, c is a hypotenuse. Find the length of the sides a, b, the angle beta if c = 5 and angle alfa = A = 35 degrees. - Surface and volume

Find the surface and volume of the rotating cone if the circumference of its base is 62.8 m and the side is 25 m long. - Maximum of volume

The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum? - There

There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie: a) AB side, b) height to side c, c) Axis of the AB side, d) median ta to side a - How many

How many m^{2}of copper sheet is needed to replace the roof of a conical tower with a diameter of 13 meters and a height of 24 meters, if we count 8% of the material for bending and waste? - 9-gon pyramid

Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm. - Digging a pit

The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m^{3}of soil were excavated when digging the pit? - Cone - side

Find the surface area and volume of the cone if its height is 125 mm and the side length is 17 cm. - Rotating cone

Find the surface and volume of the rotating cone if its side is 150 mm long and the circumference of the base is 43.96 cm. - Cone - from volume surface area

The volume of the rotating cone is 1,018.87 dm^{3}, its height is 120 cm. What is the surface area of the cone? - Calculate

Calculate the surface and volume of the cone that results from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee. - Surface of the cone

Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm^{3}. - Quadrilateral prism

The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism. - Isosceles triangle

Calculate the area of an isosceles triangle, the base of which measures 16 cm and the arms 10 cm. - Five circles

On the line segment CD = 6 there are 5 circles with radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE - Rhombus diagonals

In the rhombus ABCD are given the sizes of diagonals e = 24 cm; f = 10 cm. Calculate the side length of the diamond and the size of the angles, calculate the content of the diamond - Find the

Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm^{3}and a height of 45 cm. - Quadrilateral pyramid

The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base - Pentagonal pyramid

Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm. - The pyramid

The pyramid with a square base is 50 m high and the height of the sidewall is 80 m. Find the endge of the base of the pyramid. - Railway embankment

The section of the railway embankment is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m and the height of the embankment is 4.8 m. Calculates the size of the embankment section area. - Space diagonal angles

Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - Quadrilateral pyramid

Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture. - Ladder

How long is a ladder that touches on a wall 4 meters high and its lower part is 3 meters away from the wall? - The staircase

The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase. - Construction

Construction the triangle ABC, if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60° and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction) - Vertex points

Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area. - As shown

As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6, then the perimeter of △ BDE - Acute triangle

In the acute triangle KLM, V is the intersection of its heights and X is the heel of height to the side KL. The axis of the angle XVL is parallel to the side LM and the angle MKL is 70°. What size are the KLM and KML angles? - Gardens

The area of the square garden is 3/4 of the area of the triangular garden with sides of 80 m, 50 m, 50 m. How many meters of the fence do we need to fence a square garden? - Trapezoid 25

Trapezoid PART with AR||PT has (angle P=x) and (angle A=2x) . In addition, PA = AR = RT = s. Find the length of the median of Trapezoid PART in terms of s. - Vectors abs sum diff

The vectors a = (4,2), b = (- 2,1) are given. Calculate: a) |a+b|, b) |a|+|b|, c) |a-b|, d) |a|-|b|. - Rhombus and diagonals

The lengths of the diamond diagonals are e = 48cm, f = 20cm. Calculate the length of its sides. - Is right triangle

Find out if the triangle ABC (with right angle at the vertex C) is right if: a) a = 3dm, b = 40cm, c = 0.5m b) a = 8dm, b = 1.2m, c = 6dm - Iglu - cone tent

The cone-shaped tent is 3 m high, the diameter of its base is 3.2 m. a) The tent is made of two layers of material. How many m^{2}of fabric is needed for production (including flooring), if 20% needs to be added to the minimum amount due to cutting waste? b