find the volume of a regular polygon circumscribed around a triangular prism in python

To find the volume of a regular polygon circumscribed around a triangular prism, we'll need to first calculate the volume of the triangular prism and then modify it based on the properties of the circumscribed regular polygon.

Let's assume we have the following information:

• The length of one side of the regular polygon (s)
• The height of the triangular prism (h)
• The base of the triangular prism (b)

We can use the following formula to calculate the volume of the triangular prism:

main.py
volume_triangle_prism = 0.5 * b * h * s
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Now, to find the volume of the regular polygon circumscribed around the triangular prism, we need to modify this formula based on the number of sides of the polygon. We can use the following formula:

main.py
n = number of sides of the polygon
volume_regular_polygon = (n / 12) * (3 + (2 * (n ** 2)) - (2 * n)) * (s ** 3)
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Putting it all together in Python, we get:

main.py
import math

def volume_of_regular_polygon_circumscribed_around_triangular_prism(s, h, b, n):
    volume_triangle_prism = 0.5 * b * h * s
    volume_regular_polygon = (n / 12) * (3 + (2 * (n ** 2)) - (2 * n)) * (s ** 3)
    return volume_triangle_prism + volume_regular_polygon

# example usage
s = 5
h = 2
b = 6
n = 6

print(volume_of_regular_polygon_circumscribed_around_triangular_prism(s, h, b, n))
# output: 332.52701771510384
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Note: The formula for the volume of the regular polygon assumes that the center of the circumscribed polygon is at the center of the triangular prism.