# Equation + diagonal - practice problems

#### Number of problems found: 36

- Side wall planes

Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - 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. - Regular hexagonal prism

Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long. - Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block. - Three faces of a cuboid

The diagonal of three faces of a cuboid are 13,√281, and 20 units. Then the total surface area of the cuboid is. - A rectangle 2

A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths. - Faces diagonals

If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Ratio of sides

Calculate the area of a circle with 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. - Rectangle

There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of a rectangle. - Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm² and side is 13 cm long. - Diagonals of a rhombus 2

One diagonal of a rhombus is greater than the other by 4 cm. If the area of the rhombus is 96 cm^{2}, find the side of the rhombus. - 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. - 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. - Diagonals

What x-gon has 54 diagonals? - Solid cuboid

A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Diamond diagonals

Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm. - Ratio-cuboid

The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid. - 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. - 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? - Diamond diagonals

Calculate the diamond's diagonal lengths if its content is 156 cm² and the side length is 13 cm.

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