# 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 Formula

For a regular*n*-gon whose side length is

*L*, the formula for its area is

Area = nL

^{2}/(4*tan(180/n)),

where tan is the tangent function calculated in degrees.

**Examples**

A regular pentagon (5 sided polygon) has a side length of 10 cm. Its area is

5(10)

^{2}/(4*tan(36))

= 500/(4*0.7265425)

= 172.04774 cm

^{2}

A stop sign is an octagon because it has 8 sides. If the length of each side is 6 inches, then the area is

8(6)

^{2}/(4*tan(22.5))

= 288/(4*0.4142136)

= 173.82338 in

^{2}

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