# Pythagorean theorem + expression of a variable from formula - problems - page 4

- Cube diagonals

Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 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. - Cube and sphere

Cube with the surface area 150 cm^{2}is described sphere. What is sphere surface? - 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? - 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. T - Quadrangular prism

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

The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides. - 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. - 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. - 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. - Diagonal of the rectangle

Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm. - 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. - 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? - 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. - 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. - Diagonals of diamond

Find the area and circumference of the diamond ABCD with 15m and 11m diagonals. - Church roof 2

The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m^{2}of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste? - Axial cut

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

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

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Pythagorean theorem is the base for the right triangle calculator.