# Pythagorean theorem + expression of a variable from the formula - math problems

- Height of pyramid

The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height? - 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. - 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. - 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. - 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? - 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. - 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? - 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? - 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? - 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: - 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. - 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? - 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. - Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block. - 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). - 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 - 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 - 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? - 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. - 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

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Pythagorean theorem is the base for the right triangle calculator.