Question

A pyramid has a base that is a right triangle with legs measuring 15 cm and 24 cm. The height of the pyramid is 13 cm. What is the volume of the pyramid? Enter your answer in the box. cm³

Answer 1

`\boxed{780}\ cm^3`

Explanation:

The volume of a pyramid is given by the formula ...

V = 1/3·B·h

where B represents the area of the base and h represents the height.

The area of a triangle is given by the formula ...

A = 1/2·b·h

where b represents the length of the base of the triangle, and h represents the height of the triangle.

For a right triangle, the base and height can be taken to be the lengths of the two legs. Then we have

A = 1/2·(15 cm)·(24 cm) = 180 cm²

The volume of the pyramid is then ...

V = 1/3·(180 cm²)(13 cm) = 780 cm³

The volume of the pyramid is 780 cm³.