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

Explanation:

Step1: Calculate the area of the triangular base

The formula for the area of a triangle is (A=\frac{1}{2}\times base\times height). Here, the base of the triangle is (5) in and the height is (5) in. So, (A = \frac{1}{2}\times5\times5=\frac{25}{2}\text{ in}^2).

Step2: Find the volume of the triangular prism

The formula for the volume of a prism is (V=A\times length), where (A) is the area of the base and (length) is the length of the prism. The length of the prism is (6) in. Substitute (A = \frac{25}{2}\text{ in}^2) and (length = 6) in into the formula: (V=\frac{25}{2}\times6). [ \begin{align*} V&=\frac{25\times6}{2}\ &= 25\times3\ &=75 \end{align*} ]

Answer:

(75\text{ in}^3)