Sample

StudyMathGeometry# Regular polygon area from circumcircle

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

Area of a regular polygon is the sum of area of a triangles it contains. Area of a triangle is

,

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

.

Calculator also displays area of the circumcircle, for reference

,

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

.

Calculator also displays area of the circumcircle, for reference

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