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# Regular polygon area from circumcircle

Calculates the area of the circumcircle and of the regular polygon from radius of circumcircle and number of sides

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Area of a regular polygon is the sum of area of a triangles it contains. Area of a triangle is
$S=\frac{1}{2}absin\gamma$,
where a and b - triangle sides, and gamma is angle between those sides. For triangle in regular polygon a and b are circumradius, and gamma is 360/n, where n - number of sides. Thus area of polygon is
$S=n\frac{1}{2}r^2sin(\frac{360}{n})$.
Calculator also displays area of the circumcircle, for reference
$S=\pi r^2$

#### Regular polygon area from circumcircle

Digits after the decimal point: 2
Polygon area

Circumcircle area

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PLANETCALC, Regular polygon area from circumcircle