Pythagorean theorem + diagonal - practice problems - page 11 of 19
Number of problems found: 374
- Construct 80719
Construct a rectangle ABCD if a = 8cm and the length of the diagonal AC is 13cm. Measure the length of the sides of the rectangle. - Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm. - Diameter
If the endpoints of the diameter of a circle are A(-9, 10) and B (-5, -4), what is the circle's radius? - Construct
Construct a rhombus ABCD if the size of the diagonal AC is 6 cm and the diagonal BD is 8 cm long. - Construct 5868
Construct a square if u-a = 1 - Square side
Calculate the length of the side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0. - Billiard balls
A layer of ivory billiard balls radius of 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to everyone adjacent to it. In the spaces between sets of 4 adjacent balls, other balls rest, equal in size to the original. - Four-sided 5917
Mr. Radomír had a misfortune during the last storm; a tree fell on his roof in the shape of a regular four-sided pyramid and destroyed it all. The roof has a base edge length of 8m and a side edge length of 15m. How many m² of roofing will he have to buy? - Hexagon rotation
A regular hexagon of side 6 cm is rotated at 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated? - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Prism-shaped 6137
The prism-shaped vessel with a rhomboid base has one base diagonal of 10 cm and the edge of the base 14 cm. The edge of the base and the prism height are in a ratio of 2:5. How many liters of water is in the container when it is filled to four-fifths of t - Quadrilateral pyramid
The height of a regular quadrilateral pyramid is 6.5 cm, and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body—round calculations to 1 decimal place. - Pyramidal 44061
A pyramidal candle with a square base has a side edge of s = 12 cm and a base edge of 4 cm. How much wax will we need to make it, and how long is the wick if it is 5% bigger than its height? - Dimensions 81670
A wooden crate with dimensions d=3m, e=4m, and f=3m was placed in a transport container with dimensions a=10 m, b=4m, and c=3m. What is the maximum length of a straight, rigid rod of negligible diameter that can still be placed in the container in this si - The glass
The glass has the shape of a cylinder with an inner diameter of 12 cm, and the height from the bottom is 16 cm. The cut skewer can be inserted diagonally into the glass so it does not protrude beyond the edge. What is the largest possible length of the cu - Calculate 82567
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - 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. - 10-centimeter-high 7638
A block with a square base is inserted into a 10-centimeter-high cylinder in such a way that its base is inscribed in the base of the cylinder. The edge of the base of the block measures 4 cm. Both bodies have the same height. Calculate the difference bet - Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm, and the diagonal body forms a 50-degree angle with the base plane.
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