Chapter 12.2, Problem 9PPS

To determine

The volume of the triangular prism:

Answer to Problem 9PPS

The value of the volume of the triangular prism is $40.248f{t}^3$ .

Explanation of Solution

Given:

  $\begin{array}{l}l=9in\\ b=4in\\ a=3in\\ b_1=\frac{b}{2}=2in\end{array}$

Concept Used:

The volume of the triangular prism is given by the following expression:

  $V=\frac{1}{2}\left(l\times b\times h\right)$

Where,

Length of triangular prism: $l$

Base of triangular prism: $b$

Height of triangular prism: $h$

Calculation:

The volume of the triangular prism iscalculated by using the follwoing formula:

  $V=\frac{1}{2}\left(L\times B\times H\right)$

But the value of the height is not given, so first calculate the height of the prism by using the pythagors theorem:

  $\begin{array}{l}{h}^2+b_1{}^2=a^2\\ h^2+{\left(2\right)}^2=3^2\\ h^2=9-4\\ h^2=5\\ h=2.2360in\end{array}$

Put the given values:

  $\begin{array}{l}V=\frac{1}{2}\left(l\times b\times h\right)\\ V=\frac{1}{2}\left(9\times 4\times 2.2360\right)\\ V=40.248f{t}^3\end{array}$

Conclusion:

Hence, the volume of the triangular prism is $40.248f{t}^3$ .