find the surface area of a regular polygon circumscribed around a pyramid in python

To find the surface area of the regular polygon circumscribed around a pyramid, we need to first find the slant height of the pyramid. We can then use this slant height to find the area of each triangular face of the pyramid and add them together to get the total surface area.

Here is the code to find the surface area of a regular polygon circumscribed around a pyramid in Python:

main.py
import math

# function to find the surface area of a pyramid
def surface_area_of_pyramid(num_sides, side_length, height):
    # calculate the apothem length of the polygon
    apothem = side_length / (2 * math.tan(math.pi / num_sides))
    
    # calculate the slant height of the pyramid
    slant_height = math.sqrt(height**2 + apothem**2)
    
    # calculate the area of each triangular face
    tri_area = (num_sides * side_length * slant_height) / 2
    
    # calculate the total surface area of the pyramid
    base_area = num_sides * (side_length**2) / (4 * math.tan(math.pi / num_sides))
    total_area = tri_area + base_area
    
    return total_area
664 chars
19 lines

The function takes in three parameters: the number of sides of the regular polygon, the length of each side, and the height of the pyramid.

We first calculate the apothem length of the polygon using the formula: apothem = side_length / (2 * math.tan(math.pi / num_sides)). We then use this apothem length and the height of the pyramid to calculate the slant height using the Pythagorean theorem: slant_height = math.sqrt(height**2 + apothem**2).

We then use the number of sides, side length, and slant height to calculate the area of each triangular face of the pyramid using the formula: tri_area = (num_sides * side_length * slant_height) / 2.

Finally, we calculate the base area of the pyramid using the formula: base_area = num_sides * (side_length**2) / (4 * math.tan(math.pi / num_sides)). We add the base area to the sum of the triangular face areas to get the total surface area of the pyramid, which we return from the function.

To use this function, simply call it with the appropriate parameters:

main.py
# example usage
num_sides = 4
side_length = 3
height = 5

surface_area = surface_area_of_pyramid(num_sides, side_length, height)

print("Surface area of pyramid: ", surface_area)
179 chars
9 lines