Polygon Side Length from Area

Last modified by

KurtHeckman

on

Oct 19, 2023, 4:32:36 PM

Created by

KurtHeckman

on

Oct 19, 2023, 4:30:02 PM

$s = sqrt(((4* tan(pi/ "n" ))* "A" )/ "n" )$

$(n)"Number of Polygon Sides"$

$(A)"Area inside the polygon"$

The Math / Science

A regular n-sided polygon is a polygon with n equal length sides and is a polygon which has n equal angles at the n vertices of the polygon. This formula uses the polygon area equation:

$A = (n * s) / (4 * tan(pi/n))$ to solve for s. This is the length of a side corresponding with a polygon of n sides and an area of A. The circumference is simply stated as follows:

$"Polygon Circumference" = s * n$

Regular Polygon Information

A regular polygon is a geometric shape with three or more straight sides where every side is the same length and every angle between connecting sides are the same angle. Because of the symmetry of the regular polygon, all the vertices of the polygon can be constructed to touch a circle in which the regular polygon is inscribed and all the chords that are polygon sides will then obviously be of equal length . Likewise, because of the regular polygon's symmetry, a circle constructed to be inscribed in a regular polygon and touching the polygon will touch the regular polygon at the midpoint of the polygon side. As shown in the pictures, Figure 1 and Figure 2, lines from the regular polygon's vertices to the circle's center form n isosceles triangles of equal area.