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.py664 chars19 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.py179 chars9 lines
gistlibby LogSnag