# Incircle of a regular polygon

## Calculates the radius and area of the incircle of a regular polygon.

number of sides n
 n＝3,4,5,6....
side length a

incircle area Sc
polygon area Sp
area ratio Sc/Sp

 $\normal Incircle\ of\ regular\ polygons\\\hspace{20} n:\ number\ of\ sides\\(1)\ inradius:\hspace{50} r={\large\frac{a}{2tan{\large\frac{\pi}{n}}}}\\(2)\ incircle\ area:\hspace{10} S_c=\pi r^2={\large\frac{\pi a^2}{4tan^2({\large\frac{\pi}{n}})}}\\(3)\ polygon\ area:\hspace{10} S_p={\large\frac{1}{2}}nar={\large\frac{na^2}{4tan{\large\frac{\pi}{n}}}}\\$

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