# Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.- Quadrilateral 2

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

On the plan with a scale of 1:1500 is drawn as a square garden with area 81 cm^{2}. How many meters is long garden fence? Determine the actual acreage gardens. - 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' - 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? - Tiles

How many tiles of 20 cm and 30 cm can build a square if we have a maximum 100 tiles? - 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. - 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. - 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. - Sines

In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ) - 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. - 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. - Percentage and rectangle

About what percentage increases perimeter and area of a rectangle if both the sides 12 cm and 10 cm long we increase by 20%? - Chord distance

The circle k (S, 6 cm), calculate the chord distance from the center circle S when the length of the chord is t = 10 cm. - Trapezoid v3

The isosceles trapezoid has the angle at a firsst base 40 degrees less than the angle at second base. How large angles has this trapezoid ? - Diamond

Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm - 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. - 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? - The farmer field

The field has paralleogram shape with dimensions side a = 80 m and height 296 m. Two and two sides is at angle 80°. Calculate acreage of field in hectares. - Chors centers

The circle with a diameter 17 cm, upper chord /CD/ = 10.2 cm and bottom chord /EF/ = 7.5 cm. The midpoints of the chords H, G is that /EH/ = 1/2 /EF/ and /CG/ = 1/2 /CD/. Determine the distance between the G and H, if CD II EF (parallel). - Rectangle

The length of one side of the rectangle is three times the length of the second side. What are the dimensions of the rectangle if its circumference 96 cm?

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