Question

Identify each of the following solids. Then find the volume.

Answer 1

The given solid is:

In geometry, a triangular prism is a type of prism with three sides and two bases. The sides are of a rectangle shape and the bases are of triangle shape. Altogether, it has five faces, nine vertices, and six edges.

Notice that the given solid matches the description above.

Hence, the given solid is a triangular prism.

The Volume of a triangular prism with base area B and height h is given as:

`V=B* h`

Find the Base area B of the prism.

Notice that the base is an isosceles triangle with a base of length 12 ft and equal sides of length 20 ft.

The area B of an Isosceles triangle with base b and equal side lengths a given as:

`B=(1)/(2)* b*\sqrt[]{a^2-(b^2)/(4)}`

Substitute a=20 and b=12 into the formula:

`B=(1)/(2)*12*\sqrt[]{20^2-(12^2)/(4)}\approx114.47`

Substitute B=114.47 and h=25 into the formula for volume:

`V=114.47*25=2,861.75\text{ cubic feet}`

The volume is about 2,861.75 cubic feet.