Question

find the volume of the triangular prism. 4 in 9 in 3.5 in hint: find the area of the triangular base. then, multiply that area by the height.

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 \(b = 3.5\) in and the height of the triangle \(h=4\) in.

$$A=\frac{1}{2}\times3.5\times4=\frac{1}{2}\times14 = 7\space in^{2}$$

Step2: Calculate 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 (or height) of the prism. Here, \(A = 7\space in^{2}\) and \(l = 9\) in.

$$V=7\times9=63\space in^{3}$$

Answer:

\(63\)