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

To find the surface area of a regular polygon circumscribed around a triangular prism, we need to first calculate the perimeter of the polygon and the height of the prism. Here's the step-by-step process in Python:

1. Define the number of sides of the regular polygon as a variable n.

main.py
n = 6 # for example, for a hexagon
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2. Define the side length of the regular polygon as a variable a.

main.py
a = 5 # for example
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3. Calculate the radius r of the circumscribed circle, which is also the distance from the center of the polygon to any of its vertices. This can be done using the formula r = a / (2 * sin(pi / n)), where pi is the constant 3.14159....

main.py
from math import sin, pi

r = a / (2 * sin(pi / n))
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4. Calculate the perimeter P of the polygon, which is simply P = n * a.

main.py
P = n * a
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5. Calculate the height h of the triangular prism. This can be done by multiplying the length of one side of the triangular base by the square root of 3 (since the base is an equilateral triangle).

main.py
h = a * 3 ** 0.5 / 2 # or any other formula for calculating the height of an equilateral triangle
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6. Finally, calculate the surface area A of the polygon circumscribed around the prism using the formula A = P * h + 2 * n * r * h.

main.py
A = P * h + 2 * n * r * h
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So the complete Python program would look like this:

main.py
from math import sin, pi

n = 6 # number of sides of the hexagon
a = 5 # side length of the hexagon

r = a / (2 * sin(pi / n))
P = n * a
h = a * 3 ** 0.5 / 2
A = P * h + 2 * n * r * h

print("Surface area of the regular polygon circumscribed around a triangular prism =", A)
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