Chapter 12.4, Problem 39PPS

To determine

To find:

The volume of the regular pentagonal prism also the base area and height of each triangular prism.

Answer to Problem 39PPS

The volume of the pentagonal prism is $1100{\text{ cm}}^3$ .

Explanation of Solution

Given information:

  

The base area of one of the triangular is:

  $A=\frac{1}{2}bh$

Substitute $b=8$ and $h=5.5$ in the above formula:

  $\begin{array}{c}A=\frac{1}{2}\left(8\right)\left(5.5\right)\\ =4\left(5.5\right)\\ =22{\text{ cm}}^2\end{array}$

The height of a triangular prism is the same as the pentagonal prism:

  $h=10$

So, the volume is given as:

  $V=Bh$

Substitute $B=22$ and $h=10$ in the above formula:

  $\begin{array}{c}V=22\left(10\right)\\ =220{\text{ cm}}^3\end{array}$

Therefore, the volume of triangular prism is $220{\text{ cm}}^3$ .

Volume of the regular pentagonal prism is:

  $\begin{array}{c}V=220\cdot 5\\ =1100{\text{ cm}}^3\end{array}$

Hence the volume of the pentagonal prism is $1100{\text{ cm}}^3$ .