# Regular polygon circumcircle area

The circumcircle of a regular polygon is a circle that passes through all the vertices of the polygon. To calculate the area of the circumcircle of a regular polygon, you need to know the length of the radius of the circumcircle. Here’s the formula to calculate the area of the circumcircle of a regular polygon:

Formula for Circumcircle Radius: The radius (r) of the circumcircle of a regular polygon can be calculated using the following formula:

r = (s/2) × csc(π/n)

Where: s = Length of a side of the regular polygon n = Number of sides of the regular polygon csc = Cosecant function, which is the reciprocal of the sine function and can be calculated as 1/sin(x)

Formula for Circumcircle Area: The area (A) of the circumcircle of a regular polygon can be calculated using the following formula:

A = π × r²

Steps to Calculate Circumcircle Area:

1. Determine the length of a side of the regular polygon.
2. Count the number of sides of the regular polygon.
3. Calculate the radius of the circumcircle of the regular polygon using the formula: r = (s/2) × csc(π/n)
4. Calculate the area of the circumcircle of the regular polygon using the formula: A = π × r²

Note: π represents the mathematical constant pi, which is approximately equal to 3.14159.

I hope that helps you! Let me know if you have any further questions.