P = n s = 10s \quad,\quad a = \frac{s}{2\tan\!\left(\frac{\pi}{n}\right)} = \frac{s}{2\tan\!\left(\frac{\pi}{10}\right)}
R = \frac{s}{2\sin\!\left(\frac{\pi}{n}\right)} = \frac{s}{2\sin\!\left(\frac{\pi}{10}\right)} \quad,\quad A = \frac{n}{4}s^2 \cot\!\left(\frac{\pi}{n}\right) = \frac{5}{2}s^2 \cot\!\left(\frac{\pi}{10}\right)
\text{Equivalently: } A = \tfrac{1}{2} P a = 5 s a = 5 R^2 \sin\!\left(\tfrac{2\pi}{n}\right)=5 R^2 \sin\!\left(\tfrac{\pi}{5}\right).
\[ P = n s = 10s \quad,\quad a = \frac{s}{2\tan\!\left(\frac{\pi}{n}\right)} = \frac{s}{2\tan\!\left(\frac{\pi}{10}\right)} \] \[ R = \frac{s}{2\sin\!\left(\frac{\pi}{n}\right)} = \frac{s}{2\sin\!\left(\frac{\pi}{10}\right)} \quad,\quad A = \frac{n}{4}s^2 \cot\!\left(\frac{\pi}{n}\right) = \frac{5}{2}s^2 \cot\!\left(\frac{\pi}{10}\right) \] \[ \text{Equivalently: } A = \tfrac{1}{2} P a = 5 s a = 5 R^2 \sin\!\left(\tfrac{2\pi}{n}\right)=5 R^2 \sin\!\left(\tfrac{\pi}{5}\right). \] Interior angle \(= 180^\circ - \tfrac{360^\circ}{n} = 144^\circ\), central angle \(= \tfrac{360^\circ}{n} = 36^\circ\).