# Diagonal + Pythagorean theorem - math problems

#### Number of problems found: 220

• Regular square prism
The volume of a regular square prism is 192 cm3. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism.
• Triangular land
Jana has a rectangular garden measuring 30 meters by 72 meters that she wants to split diagonally from corner to corner using a fence. How long does her fence need to be?
• Angle of diagonals
Calculate the perimeter and the area of a rectangle if its diagonal is 14 cm and the diagonals form an angle of 130°.
• The diamond
The diamond has an area S = 120 cm2, the ratio of the length of its diagonals is e: f = 5: 12. Find the lengths of the side and the height of this diamond.
• Side and diagonal
Find the circumference and the area of the rectangle if given: side a = 8 cm diagonal u = 10 cm.
• Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.
• Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid.
• Diagonals of a prism
The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal with the diagonal of the base.
• Surface and volume - cube
Find the surface and volume of a cube whose wall diagonal is 5 cm long.
• Metal washers
Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. Calculate the percentage of material waste if no material is lost when two adjacent circles meet.
• Body diagonal
Calculate the length of the body diagonal of a block with dimensions: a = 20 cm, b = 30 cm, c = 15 cm.
• Total area
Calculate the total area (surface and bases) of a prism whose base is a rhombus which diagonals of 12cm and 18cm and prism height is 10 cm.
• Rhombus and diagonals
The lengths of the diamond diagonals are e = 48cm, f = 20cm. Calculate the length of its sides.
• Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.
• Cuboid diagonals
The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.
• Rhombus diagonals
In the rhombus ABCD are given the sizes of diagonals e = 24 cm; f = 10 cm. Calculate the side length of the diamond and the size of the angles, calculate the content of the diamond
The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism.
• Body diagonal
Find the length of the body diagonal of a cuboid with lengths of 16 cm, 7 cm, and 4 cm.
• Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.