Question

the volume of this triangular prism is 616 cubic inches. what is the value of g? 11 in 16 in g = \square inches submit

Explanation:

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

The volume \( V \) of a triangular prism is given by the formula \( V=\frac{1}{2}\times\text{base}\times\text{height}\times\text{length} \), where the base and height are the base and height of the triangular face, and the length is the length of the prism. Here, the base of the triangle is \( 11 \) inches, the height of the triangle is \( g \) inches, and the length of the prism is \( 16 \) inches, and the volume \( V = 616 \) cubic inches. So we have the equation:
\[
616=\frac{1}{2}\times11\times g\times16
\]

Step2: Simplify the right - hand side of the equation

First, calculate \( \frac{1}{2}\times16 = 8 \). Then the equation becomes:
\[
616 = 11\times g\times8
\]
\[
616=88g
\]

Step3: Solve for \( g \)

To find \( g \), we divide both sides of the equation \( 616 = 88g \) by \( 88 \):
\[
g=\frac{616}{88}
\]
\[
g = 7
\]

Answer:

\( 7 \)