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In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter is fixed, or a regular apeirogon, if the edge length is fixed.

Area = perimeter * apothem(*)2
(*) The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides.
Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides.
apothem = side2 * tan(180 / n)

perimeter = side * n

when n is the number of sides.




A = p * a2 =
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