homechevron_rightStudychevron_rightMathchevron_rightGeometry

Side of regular polygon from polygon area

Calculates the side length of regular polygon given the area of the regular polygon and number of sides

This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/3688/. Also, please do not modify any references to the original work (if any) contained in this content.

We need to find side length of regular polygon given its area and number of sides.
As it was written in Regular polygon area from circumcircle, the dependence of polygon area from circumradius is
$S=n\frac{1}{2}r^2sin(\frac{360}{n})$.
$r=\sqrt{ \frac{2S}{n sin(\frac{360}{n})} }$.
And half of side is the opposite leg of the triangle of radius and altitude to this side from the center
$l=2r sin(\frac{360}{2n})} }$

Side of regular polygon from polygon area

Digits after the decimal point: 2