find the surface area of a regular polygon inscribed in a cone in python

To find the surface area of a regular polygon inscribed in a cone, we need to follow the below steps:

1. Find the slant height of the cone (l) using Pythagorean theorem. This can be done using the radius (r) and height (h) of the cone, as l = sqrt(r^2 + h^2).
2. Find the perimeter of the regular polygon (P) using the number of sides (n) and the length of one side (s), as P = n*s.
3. Find the apothem of the regular polygon (a) using the radius (r) and the number of sides (n), as a = r*cos(pi/n).
4. Find the surface area of the regular polygon (A) using the perimeter (P) and apothem (a), as A = (1/2)*P*l + n*a*l.

Below is the Python code to implement the above steps:

main.py
import math

def surface_area_regular_polygon_inscribed_cone(n, r, h):
    s = 2*r*math.sin(math.pi/n)
    l = math.sqrt(r**2 + h**2)
    P = n*s
    a = r*math.cos(math.pi/n)
    A = 0.5*P*l + n*a*l
    return A
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Here, n is the number of sides of the regular polygon, r is the radius of the cone, and h is the height of the cone.

We use the math module in Python to perform mathematical calculations, such as square roots (sqrt), trigonometric functions (sin and cos), and pi (pi). The function surface_area_regular_polygon_inscribed_cone takes in the parameters n, r, and h, and returns the surface area of the regular polygon inscribed in the cone.