The formula to calculate the Diagonal across M sides of N-gon (dm) is:
\[ d_{m} = \frac{l_{e} \cdot \sin\left(\frac{\pi \cdot M_{Sides}}{N_{Sides}}\right)}{\sin\left(\frac{\pi}{N_{Sides}}\right)} \]
Diagonal across M sides of N-gon is defined as the length of the diagonal across N sides of an N-sided polygon. It is measured in Meter.
Let's assume the following values:
Using the formula:
\[ d_{m} = \frac{10 \cdot \sin\left(\frac{\pi \cdot 6}{8}\right)}{\sin\left(\frac{\pi}{8}\right)} \approx 18.4775906502257 \]
The Diagonal across M sides of N-gon is approximately 18.4775906502257 Meter.
| Edge Length (Meter) | Diagonal across M sides (Meter) |
|---|---|
| 5 | 9.238795325112868 |
| 6 | 11.086554390135442 |
| 7 | 12.934313455158014 |
| 8 | 14.782072520180590 |
| 9 | 16.629831585203164 |
| 10 | 18.477590650225736 |
| 11 | 20.325349715248311 |
| 12 | 22.173108780270883 |
| 13 | 24.020867845293459 |
| 14 | 25.868626910316028 |
| 15 | 27.716385975338603 |