Question

Derive and apply a formula for the volume of a right prism

The Truit family rented the cabin shown in the shape of a triangular prism. The cabin is 30 feet deep. What is its volume?
25 ft
and
15 ft

Answer 1

The formula for the volume of a right prism is given by:

Volume = Base area x Height

In this case, the base of the triangular prism is a triangle, and its area can be calculated using the formula:

Base area = (1/2) x Base x Height

where Base and Height are the dimensions of the triangular base.

So, to find the volume of the cabin, we can use the following steps:

Calculate the area of the triangular base: Base area = (1/2) x Base x Height Base area = (1/2) x 25 ft x 15 ft Base area = 187.5 sq ft

Multiply the area of the base by the height of the prism: Volume = Base area x Height Volume = 187.5 sq ft x 30 ft Volume = 5625 cubic feet

Therefore, the volume of the cabin is 5625 cubic feet.