The pentagonal prism below has a base area of 42 unitssquared 2 and a volume of 331.8 unitscubed 3 . Find its height.

1. Break Down the Problem

To find the height of a pentagonal prism, we need to use the formula for the volume of a prism: $\text{Volume} = \text{Base Area} \times \text{Height}$ Given the volume and the base area, we can rearrange this formula to find the height.

2. Relevant Concepts

• Volume of a prism: $V = A \times h$ Where:
• $V$ = volume
• $A$ = area of the base
• $h$ = height of the prism

3. Analysis and Detail

From the problem statement:

• Volume $V = 331.8 \, \text{units}^3$
• Base Area $A = 42 \, \text{units}^2$

Now we can rearrange the volume formula to find the height: $h = \frac{V}{A}$ Substituting the values: $h = \frac{331.8}{42}$

4. Verify and Summarize

Calculating the height: $h = \frac{331.8}{42} = 7.9 \, \text{units}$ We can verify by multiplying the base area and the height to see if we return to the original volume: $42 \times 7.9 = 331.8 \, \text{units}^3$ This confirms our calculation is accurate.

Final Answer

The height of the pentagonal prism is $7.9 \, \text{units}$.