The formula to calculate the Base Area of a Pentagonal Prism is:
\[ A_{\text{Base}} = \frac{\sqrt{5 \left(5 + 2 \sqrt{5}\right)}}{4} \cdot \left(\text{Base Edge Length}\right)^2 \]
The Base Area of a Pentagonal Prism is the total amount of two-dimensional space occupied by the base face of the prism. The Base Edge Length is the length of the straight line connecting any two adjacent vertices of the base.
Let's assume the following value:
Using the formula:
\[ A_{\text{Base}} = \frac{\sqrt{5 \left(5 + 2 \sqrt{5}\right)}}{4} \cdot 10^2 \approx 172.0477 \]
The Base Area is approximately 172.0477 Square Meters.
| Base Edge Length (Meters) | Base Area (Square Meters) |
|---|---|
| 9 | 139.358669447706319 |
| 9.5 | 155.273085403154255 |
| 10 | 172.047740058896693 |
| 10.5 | 189.682633414933605 |
| 11 | 208.177765471264991 |