Question

What is the volume of this triangular prism?

A triangular prism has length 16 feet, width 4 feet and height 9 feet.

A.

B.

C.

D.

Answer 1

To find the volume of a triangular prism, you can use the formula:

\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]

where the base area is the area of the triangular base and the height is the length of the prism.

1. **Determine the base area of the triangle**:

The base of the triangle is the width (4 feet), and the height of the triangle (the vertical height from the base to the top vertex) is given as 9 feet. The area of a triangle is calculated with the formula:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

In this case:

- Base = 4 feet
- Height = 9 feet

Calculating the area:

\[
\text{Area} = \frac{1}{2} \times 4 \times 9 = \frac{1}{2} \times 36 = 18 \text{ square feet}
\]

2. **Calculate the volume of the prism**:

Now that we have the area of the base, we can find the volume by multiplying the base area by the length (which is 16 feet):

\[
\text{Volume} = \text{Base Area} \times \text{Length} = 18 \text{ square feet} \times 16 \text{ feet}
\]

Calculating the volume:

\[
\text{Volume} = 18 \times 16 = 288 \text{ cubic feet}
\]

Thus, the volume of the triangular prism is **288 cubic feet**.