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

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Article : Side of regular polygon from polygon area - Author, Translator ru - en
Calculator : Side of regular polygon from polygon area - Author, Translator ru - en

Created: 2014-06-15 08:10:09, Last updated: 2020-11-03 14:19:31

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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
$S=n\frac{1}{2}r^2sin(\frac{360}{n})$ .
Thus, circumradius will be
$r=\sqrt{ \frac{2S}{n sin(\frac{360}{n})} }$ .
And half of side is the opposite leg of the triangle of radius and altitude to this side from the center
$l=2r sin(\frac{360}{2n})} }$