Math.by - The regular polygon area

The regular polygon area

Enter the known data:

 n = - amount of sides a = - length of side r = - radius of inscribed circle R = - radius of circumscribed circle

S =

Theory

$S=\frac{n}{4} a^2 ctg(\frac{\pi}{n})$

$S=\frac{n}{2} R^2 \sin{\frac{2\pi}{n}}$

$S=\frac{n R a}{2}$

a - side length of regular polygon, n - amount of sides, r - radius of inscribed circle, R - radius of circumscribed circle.