# Right triangle - math word problems

1. Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
2. Pyramid
The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
3. Cone
The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
4. Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
5. Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
6. Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
7. Flowerbed
Family cultivated tulips on a square flower bed of 6 meters. Later they added the square terrace with a side of 7 meters to their house. One vertex of the terrace lay exactly in the middle of a tulip bed, and one side of the terrace divided the side of th
8. Rhombus OWES
OWES is a rhombus given that OW 6cm and one diagonal measures 8cm. Find its area?
9. Cube
Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.
10. Cuboid - volume, diagonals
The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?
11. Circular ring
Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form.
12. Body diagonal
Find the cube surface if its body diagonal has a size of 6 cm.
13. Circumscribed circle to square
Find the length of a circle circumscribing a square of side 10 cm. Compare it to the perimeter of this square.
14. Prism - box
The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.
15. Concrete block
Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters.
16. Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
17. Inscribed circle
XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
18. Rectangular trapezium
Calculate the perimeter of a rectangular trapezium when its content area is 576 cm2 and sice a (base) is 30 cm, height 24 cm.
19. Cone container
Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
20. Octagonal mat
Octagonal mat formed from a square plate with a side of 40 cm so that every corner cut the isosceles triangle with leg 3.6 cm. What is the content area of one mat?

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