Regular Polygon Circumcircle Area Calculator

Any plane geometry figure that is bounded by straight lines connecting to form a closed shape is termed as the polygon. A regular polygon is one whose sides and angles are equal. A circle touching all the vertices of a triangle or polygon is known as circumcircle. The below given online Regular Polygon Circumcircle Area calculator assists you to find the area of the circumcircle that is formed on a regular polygon using the number of sides and length of the side.

Any plane geometry figure that is bounded by straight lines connecting to form a closed shape is termed as the polygon. A regular polygon is one whose sides and angles are equal. A circle touching all the vertices of a triangle or polygon is known as circumcircle. The below given online Regular Polygon Circumcircle Area calculator assists you to find the area of the circumcircle that is formed on a regular polygon using the number of sides and length of the side.

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Formula:

Circumradius (r) = l / (2 x sin( π / n )) Area of the polygon = ( n x l2 ) / ( 4 x tan( π / n ) ) Regular Polygon Circumcircle Area = 3.14 x r2 Where, n = Number of sides of the polygon, r = circumradius, l = Length of the side of the polygon

Example:

A regular polygon has 8 sides with each side having a length of 5 cm.

Solution,

Circumradius (r) = l / (2 x sin( π / n ))
= 5/(2 x sin (3.14 / 8))
= 6.53 cm
Area of the polygon = ( n x l2 ) / ( 4 x tan( π / n ) )
= (n x 52) / (4 x tan(3.14 / 8)
= 120.657 cm2
Circumcircle Area = 3.14 x r2
= 3.14 x 6.532
= 134.028 cm2

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