Polygon
Regular polygons

Many specialized formulas apply to the areas of regular polygons.

The area of a regular polygon is given in terms of the radius r of its inscribed circle and its perimeter p by

This radius is also termed its apothem and is often represented as a.

The area of a regular n -gon in terms of the radius R of its circumscribed circle can be expressed trigonometrically as:

The area of a regular n -gon inscribed in a unit-radius circle, with side s and interior angle α, {\displaystyle \alpha,} can also be expressed trigonometrically as:
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