Regular Polygon Formulas

Regular Polygon Formulas

Side: a

Number of sides: n

Internal angle: $\alphs$

Slant height: m

Radius of circumscribed circle: R

Perimeter: L

Semi perimeter: p

Area: S

1. $\alpha = \frac{n - 2}{2}\cdot 180^{\circ}$

2. $R = \frac{a}{2sin\frac{\pi }{4}}$

3. r = m = $\frac{a}{2tan\frac{\pi}{n} }= \sqrt{R^{2} - \frac{a^{2}}{4}}$

4. L =na

5. S = $\frac{nR^{2}}{2}sin\frac{2\pi }{n},$
$S = pr = p\sqrt{R^{2} - \frac{a^{2}}{4}}$
Where p = $\frac{L}{2}$