Question

find the volume of this triangular prism. be sure to include the correct unit in your answer.

Explanation:

Step1: Recall the formula for the volume of a triangular prism

The volume \( V \) of a triangular prism is given by the formula \( V = \text{Area of the triangular base} \times \text{length of the prism} \). The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \).

Step2: Calculate the area of the triangular base

The base of the triangle is \( 6 \) in and the height of the triangle is \( 9 \) in. So the area of the triangular base \( A = \frac{1}{2} \times 6 \times 9 \).
\[
A=\frac{1}{2}\times6\times9 = 3\times9=27 \text{ square inches}
\]

Step3: Calculate the volume of the triangular prism

The length of the prism (the distance along the direction perpendicular to the triangular base) is \( 10 \) in. Using the volume formula \( V = A\times \text{length} \), we substitute \( A = 27 \) and length \( = 10 \).
\[
V=27\times 10 = 270 \text{ cubic inches}
\]

Answer:

\( 270 \text{ in}^3 \)