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

main.py
import math

def surface_area_of_polygon_in_cylinder(num_sides, side_length, height):
    # Calculate the polygon perimeter and apothem
    perimeter = num_sides * side_length
    apothem = side_length / (2 * math.tan(math.pi / num_sides))
    
    # Calculate the polygon area and the area of the cylinder top and bottom
    polygon_area = 0.5 * perimeter * apothem
    top_bottom_area = math.pi * (side_length / (2 * math.sin(math.pi / num_sides))) ** 2
    
    # Calculate the surface area of the cylinder
    surface_area = perimeter * height + 2 * polygon_area + 2 * top_bottom_area
    
    return surface_area
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main.py
surface_area = surface_area_of_polygon_in_cylinder(6, 5, 10)
print(surface_area) # Output: 642.2492214274281
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