The formula to calculate the Area of a Regular Polygon given the Inradius is:
\[ A = \text{Inradius}^2 \cdot \text{Number of Sides} \cdot \tan\left(\frac{\pi}{\text{Number of Sides}}\right) \]
The Area of a Regular Polygon is the total region or space enclosed inside the polygon. The Inradius is the line connecting the center of the polygon to the midpoint of one of its sides, also the radius of the incircle. The Number of Sides denotes the total number of sides of the polygon.
Let's assume the following values:
Using the formula:
\[ A = 12^2 \cdot 8 \cdot \tan\left(\frac{\pi}{8}\right) \approx 477.1740 \]
The Area is approximately 477.1740 Square Meters.
| Number of Sides | Inradius (Meters) | Area (Square Meters) |
|---|---|---|
| 7 | 12 | 485.427215757988847 |
| 7.5 | 12 | 480.846980133219006 |
| 8 | 12 | 477.174023853805465 |
| 8.5 | 12 | 474.180126195841638 |
| 9 | 12 | 471.705423608998217 |