How to Calculate the Area of a Regular N Sides Polygon Inside a Circle of Radius R in Python

The challenge

Write the following function:

def area_of_polygon_inside_circle(circle_radius, number_of_sides):

It should calculate the area of a regular polygon of numberOfSides, number-of-sides, or number_of_sides sides inside a circle of radius circleRadius, circle-radius, or circle_radius which passes through all the vertices of the polygon (such a circle is called circumscribed circle or circumcircle). The answer should be a number rounded to 3 decimal places.

Input/Output Examples

area_of_polygon_inside_circle(3, 3) # returns 11.691
area_of_polygon_inside_circle(5.8, 7) # returns 92.053
area_of_polygon_inside_circle(4, 5) # returns 38.042

The solution in Python code

Option 1:

from math import sin, pi

def area_of_polygon_inside_circle(r, n):
    return round(0.5 * n * r ** 2 * sin(2 * pi / n), 3)

Option 2:

import math
def area_of_polygon_inside_circle(circle_radius, number_of_sides):
    r = circle_radius
    s = number_of_sides
    a = (s * (r ** 2) * math.sin(2*math.pi/s))/2
    return round(a, 3)

Option 3:

from math import sin,cos,radians
def area_of_polygon_inside_circle(circle_radius, number_of_sides):
    angle = radians(360/(number_of_sides*2))
    opposite = circle_radius*sin(angle)
    adjacent = circle_radius*cos(angle)
    return round(adjacent*opposite*number_of_sides,3)

Test cases to validate our solution

test.describe('Example Tests')
test.it('ex1')
test.assert_equals(area_of_polygon_inside_circle(3, 3), 11.691)
test.it('ex2')
test.assert_equals(area_of_polygon_inside_circle(2, 4), 8)
test.it('ex3')
test.assert_equals(area_of_polygon_inside_circle(2.5, 5), 14.86)