Question

What is the volume of this triangular prism?

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


576 ft^3

288 ft^3

34 ft^3

29 ft^3

Answer 1

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

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

For a triangular prism, the base area is given by the formula for the area of a triangle:

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

In this case, we have:

- Base (width) = 4 feet
- Height of the triangle = 9 feet
- Length of the prism = 16 feet

First, calculate the base area:

\[
\text{Base Area} = \frac{1}{2} \times 4 \, \text{ft} \times 9 \, \text{ft} = \frac{1}{2} \times 36 \, \text{ft}^2 = 18 \, \text{ft}^2
\]

Now, calculate the volume of the prism:

\[
\text{Volume} = 18 \, \text{ft}^2 \times 16 \, \text{ft} = 288 \, \text{ft}^3
\]

Thus, the volume of the triangular prism is \( \boxed{288 \, \text{ft}^3} \).