Question

Find the volume of the triangular prism above the base is 13 inches. The width is 18 inches and the height is 7 inches.

Answer 1

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

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

For a triangular prism, the base area can be calculated using the formula for the area of a triangle:

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

In your case, you provided:

- The base of the triangular base = 13 inches
- The height of the triangle = 7 inches
- The width (or length) of the prism = 18 inches

First, we calculate the area of the triangular base:

\[
\text{Base Area} = \frac{1}{2} \times 13 \times 7
\]
\[
\text{Base Area} = \frac{1}{2} \times 91 = 45.5 \text{ square inches}
\]

Next, we calculate the volume of the prism:

\[
\text{Volume} = \text{Base Area} \times \text{Width (length of the prism)}
\]
\[
\text{Volume} = 45.5 \times 18
\]
\[
\text{Volume} = 819 \text{ cubic inches}
\]

Therefore, the volume of the triangular prism is **819 cubic inches**.