Question

find the volume of this triangular prism.
be 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 \( b = 7\) in and the height of the triangle \( h=9\) in.

$$ A=\frac{1}{2}\times7\times9=\frac{63}{2}= 31.5\text{ in}^2 $$

Step2: Find the volume of the triangular prism

The formula for the volume of a prism is \( V=A\times l\), where \( A\) is the area of the base and \( l\) is the length of the prism. The length of the prism \( l = 9\) in (the distance between the two triangular bases).

$$ V=31.5\times9 = 283.5\text{ in}^3 $$

Answer:

\(283.5\text{ in}^3\)