To find the volume of a regular polygon inscribed in a triangular prism, we can follow these steps:
area = (1/2) * perimeter * apothem
.volume = area * height
.Here's the implementation in Python:
main.py611 chars21 lines
In this implementation, we use the math
module to perform the necessary calculations. After defining the number of sides and length of the polygon, we calculate the apothem length using the formula apothem_length = side_length / (2 * math.tan(math.pi / num_sides))
. Then, we find the polygon perimeter and use it to calculate the polygon area.
Next, we calculate the height of the triangular prism. We obtain the base of the triangle by multiplying the side length by the number of sides, and the height is calculated using the formula for equilateral triangles. Finally, we find the difference between the triangle height and the apothem length to get the height of the prism.
Finally, we find the volume of the prism by multiplying the area of the polygon by the height of the prism.
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