Question

the volume of this triangular prism is 996 cubic inches. what is the value of v? 12 in 16.6 in v v = inches

Explanation:

Step1: Recall volume formula

The volume formula for a triangular prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height of the prism. The base is a triangle with base $b = 12$ in and height $h_{triangle}=16.6$ in, so the area of the base $B=\frac{1}{2}\times12\times16.6$. And the height of the prism is $v$.

Step2: Calculate base - area

$B=\frac{1}{2}\times12\times16.6 = 6\times16.6=99.6$ square - inches.

Step3: Solve for $v$

Since $V = Bh$ and $V = 996$ cubic - inches, $B = 99.6$ square - inches, we have $996=99.6v$. Then $v=\frac{996}{99.6}$.
$v = 10$ inches.

Answer:

10