area of a regular polygon

Area of a Regular Polygon

The area of a regular polygon is given by the formula below.

area = (½)(apothem)(perimeter)


Several other area formulas are also available.


Regular Polygon Formulas

n = number of sides
s = length of a side
r = apothem (radius of inscribed circle)   
R = radius of circumcircle

Sum of interior angles = (n – 2)·180°

Interior angle =

Area = (½)nsr

Regular Pentagon

Regular Hexagon

Regular Heptagon

Regular Octagon

Regular Nonagon


See also

Area of a convex polygon

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