Area of shape + Pythagorean theorem - math problems

Area is the quantity that expresses the extent of a two-dimensional shape. The area can be understood as the amount of paint necessary to cover the surface with a single coat. The area of a shape can be measured by comparing the shape to squares of a fixed size 1 m^2 or 1 cm^2 etc. Every unit of length has a corresponding unit of area. Areas can be measured in square metres (m^2), square centimetres (cm^2), square millimetres (mm^2), square kilometres (km^2), square feet (ft^2), square yards (yd^2), square miles (mi^2), and so forth.

Number of problems found: 195

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.
Isosceles triangle
Calculate the area of an isosceles triangle, the base of which measures 16 cm and the arms 10 cm.
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 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.
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.
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.
The right triangle
The right triangle ABC has a leg a = 36 cm and an area S = 540 cm². Calculate the length of the leg b and the median t2 to side b.
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?
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?
Horses playground
The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m², 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?
Compute 4
Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
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.
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 cm³ (l).
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
Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm². 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
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´.
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
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.
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.
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?