Area of a Regular Polygon with n Sides
A regular polygon is a convex plane figure in which all the sides have equal length and all of the interior angles have equal measure. The area of a regular polygon depends on the number of sides and the length of the sides. If you know these two values, you can plug them into a trigonometric formula to compute the area. You can also use the convenient geometry calculator below.
Regular Polygon Area FormulaFor a regular n-gon whose side length is L, the formula for its area is
Area = nL2/(4*tan(180/n)),
where tan is the tangent function calculated in degrees.
A regular pentagon (5 sided polygon) has a side length of 10 cm. Its area is
= 172.04774 cm2
A stop sign is an octagon because it has 8 sides. If the length of each side is 6 inches, then the area is
= 173.82338 in2
© Had2Know 2010