Question

The Smith family bought a new tent for a camping trip.

A triangular prism. The triangular base has a base of 9 feet and height of 7 feet. The height of the prism is 15 feet.

What is the volume of their new tent?
135 ftmc010-2.jpg
470.5 ftmc010-3.jpg
472.5 ftmc010-4.jpg
945 ftmc010-5.jpg

Answer 1

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

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

1. First, calculate the area of the triangular base. The area \( A \) of a triangle is given by the formula:

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

In this case:
- Base = 9 feet
- Height = 7 feet

Substituting in the values:

\[
A = \frac{1}{2} \times 9 \times 7 = \frac{1}{2} \times 63 = 31.5 \text{ square feet}
\]

2. Now, use this area to find the volume of the prism. The height of the prism is 15 feet. We substitute the base area and the height of the prism into the volume formula:

\[
\text{Volume} = 31.5 \text{ square feet} \times 15 \text{ feet} = 472.5 \text{ cubic feet}
\]

Thus, the volume of the Smith family's new tent is **472.5 cubic feet**.

So the correct answer is **472.5 ft³ (option 472.5)**.