# Regular Circumcircle Polygon Area Calculator

The calculator calculates the area of a regular polygon given the circumradius and number of sides and displays it along with the area of the circumcircle.

### This page exists due to the efforts of the following people:

#### Timur

Created: 2011-07-21 15:01:20, Last updated: 2023-03-20 13:30:56

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To use the calculator, the user enters the circumradius and the number of sides of the regular polygon. The calculator calculates the area of the regular polygon and the area of the circumcircle, and displays them for comparison.

The area of a regular polygon is the sum of the areas of the triangles it contains.

The area of a triangle is

$S=\frac{1}{2}absin\gamma$
where a and b are triangle sides, and γ is the angle between those sides.

For the triangle which is a part of a regular polygon, each side is a circumradius, and γ is 360/n, where n is the number of sides.

Thus area of polygon is

$S=n\frac{1}{2}r^2sin(\frac{360}{n})$

The area of the circumcircle calculates as

$S=\pi r^2$

#### Regular polygon area from circumcircle

Digits after the decimal point: 2
Polygon area

Circumcircle area

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PLANETCALC, Regular Circumcircle Polygon Area Calculator