The formula to calculate the Inradius of a Regular Polygon is:
\[ r_i = r_c \cdot \cos\left(\frac{\pi}{N}\right) \]
The inradius of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides. The circumradius is the radius of the circumcircle that touches each vertex of the polygon. The number of sides is the total number of sides of the polygon.
Let's assume the following values:
Using the formula:
\[ r_i = 13 \cdot \cos\left(\frac{\pi}{8}\right) \approx 12.0104 \]
The Inradius is approximately 12.0104 Meters.
| Circumradius (Meters) | Number of Sides | Inradius (Meters) |
|---|---|---|
| 12 | 8 | 11.086554390135440 |
| 12.5 | 8 | 11.548494156391085 |
| 13 | 8 | 12.010433922646728 |
| 13.5 | 8 | 12.472373688902371 |
| 14 | 8 | 12.934313455158014 |