The formula to calculate the Area of a Regular Polygon given its perimeter and circumradius is:
\[ \text{Area} = \frac{\text{Perimeter} \times \sqrt{\text{Circumradius}^2 - \frac{\text{Edge Length}^2}{4}}}{2} \]
The Area of a Regular Polygon is the total region or space enclosed inside the polygon. The Perimeter of a Regular Polygon is the total distance around the edge of the polygon. The Circumradius of a Regular Polygon is the radius of a circumcircle touching each of the polygon's vertices. The Edge Length of a Regular Polygon is the length of one of the sides of the polygon.
Let's assume the following values:
Using the formula:
\[ \text{Area} = \frac{80 \times \sqrt{13^2 - \frac{10^2}{4}}}{2} \approx 480 \, \text{square meters} \]
The Area of the Regular Polygon is approximately 480 square meters.
| Perimeter (meters) | Area (square meters) |
|---|---|
| 70 | 420.000000000000000 |
| 75 | 450.000000000000000 |
| 80 | 480.000000000000000 |
| 85 | 510.000000000000000 |
| 90 | 540.000000000000000 |