The formula to calculate the Base Area of a Pentagonal Pyramid given its edge length is:
\[ \text{Base Area} = \frac{1}{4} \cdot \sqrt{5 \cdot (5 + 2\sqrt{5})} \cdot \text{Edge Length}^2 \]
The Base Area of a Pentagonal Pyramid is the total amount of two-dimensional space occupied on the base surface of the pentagonal pyramid. The edge length of the base of the pentagonal pyramid is the length of the straight line connecting any two adjacent vertices of the base.
Let's assume the following value:
Using the formula:
\[ \text{Base Area} = \frac{1}{4} \cdot \sqrt{5 \cdot (5 + 2\sqrt{5})} \cdot 10^2 \approx 172.0477 \, \text{square meters} \]
The Base Area is approximately 172.0477 square meters.
| Edge Length (meters) | Base Area (square meters) |
|---|---|
| 8 | 110.110553637693883 |
| 9 | 139.358669447706319 |
| 10 | 172.047740058896693 |
| 11 | 208.177765471264991 |
| 12 | 247.748745684811240 |