Area + diagonal - practice problems
Number of problems found: 147
- 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.
- A prism
A prism with an altitude of 15cm has a base in the form of a regular octagon inscribed in a square 10cmx10cm. Find the volume of the prism.
- Trapezoid and diagonals
Find the area of a trapezoid with bases a = 24 cm, c = 16 cm and diagonals u = 22 cm, v = 26 cm.
- The area
The area of a rhombus is 143 m². If the longer diagonal is 26 m, find the shorter diagonal in inches named d1.
- Parallelogram diagonals
Find the area of a parallelogram if the diagonals u1 = 15 cm, u2 = 12 cm and the angle formed by them is 30 degrees.
- 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.
- 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.
- A rhombus 2
A rhombus have sides of 170 meters and diagonal of 300 meters. What is the area of the rhombus?
- 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.
- 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.
- 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 are 10 cm.
- 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.
- Quadrilateral prism
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.
- Quadrilateral pyramid
In a regular quadrilateral pyramid, the height 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.
- Quadrilateral oblique prism
What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°.
Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
Area - practice problems. Diagonal - practice problems.