Chapter 12, Problem 5E

To determine

To find: The area of the base of oblique pentagonal prism.

Answer to Problem 5E

Thebase area of oblique pentagonal prism is $8{\text{cm}}^2$ .

Explanation of Solution

Given information:It is given that the volume of oblique pentagonal prism is $96{\text{cm}}^3$ and the lateral edge is $24\text{cm}$ .

  

Calculation:

Draw the figure $\Delta ABC$ such that $AB=h$ , $AC=l$ .

  

Here, $h$ is height of the oblique pentagonal prism and $l$ is the lateral side of the prism.

Height of the oblique pentagonal prism can be calculated as:

  $\text{sin}\theta =\frac{h}{l}$

Substitute 24 for $l$ and $\theta =30°$ in the above formula.

  $\begin{array}{c}\text{sin}\left(30°\right)=\frac{h}{24}\\ h=24\times 0.5\\ h=12\text{cm}\end{array}$

The formula for the volume of the pentagonal prism is:

  $\text{Volume}=\left(\text{base}\text{area}\right)\cdot \text{height}$

Substitute $96{\text{cm}}^3$ for volume and 12 for height in the above formula.

  $\begin{array}{c}96=\left(\text{base}\text{area}\right)\cdot 12\\ \text{base}\text{area}=\frac{96}{12}\\ =8{\text{cm}}^2\end{array}$

Therefore, the base area of oblique pentagonal prism is $8{\text{cm}}^2$ .