Question

A prism with a triangular base has a volume of 432 cubic feet. The height of the prism is 8

feet and the triangle base has a base of 12 feet. Find the height of the triangular base of the
prism.​

Answer 1

9 feet

Explanation:

Given:

A prism with a triangular base has a volume of 432 cubic feet.

The height of the prism is 8.

The triangle base has a base of 12 feet.

Question asked:

The height of the triangular base of the prism = ?

solution:

Volume of triangular prism =
`Area of triangle * height`

`432 = Area of triangle *8`

Dividing both side by 8

`54 = Area of triangle`

`54 =`
`(1)/(2) * base * height`

`54 = (1)/(2) *12* height\\54 = (12)/(2) * height`

Multiplying both side by 2

`108 = 12 * height`

Dividing both side by 12

`9 = height`

Thus, height of the triangular base of the prism is 9