The challenge

Write the following function:

 ``````1 `````` ``````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

 ``````1 2 3 `````` ``````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:

 ``````1 2 3 4 `````` ``````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:

 ``````1 2 3 4 5 6 `````` ``````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:

 ``````1 2 3 4 5 6 `````` ``````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

 ``````1 2 3 4 5 6 7 `````` ``````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) ``````