The formula to calculate the Perimeter of a Regular Polygon given the Number of Sides and Inradius is:
\[ P = 2 \cdot \text{Number of Sides} \cdot \text{Inradius} \cdot \tan\left(\frac{\pi}{\text{Number of Sides}}\right) \]
The Perimeter of a Regular Polygon is the total distance around the edge of the polygon. The Number of Sides denotes the total number of sides of the polygon, and 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.
Let's assume the following values:
Using the formula:
\[ P = 2 \cdot 8 \cdot 12 \cdot \tan\left(\frac{\pi}{8}\right) \approx 79.5290 \]
The Perimeter is approximately 79.5290 Meters.
| Number of Sides | Inradius (Meters) | Perimeter (Meters) |
|---|---|---|
| 7 | 12 | 80.904535959664813 |
| 7.5 | 12 | 80.141163355536492 |
| 8 | 12 | 79.529003975634254 |
| 8.5 | 12 | 79.030021032640278 |
| 9 | 12 | 78.617570601499708 |