To find the volume of a regular polygon inscribed in a pyramid, we need to know two things: the height of the pyramid (from the apex to the base), and the area of the base polygon. We can then use the formula V = (1/3)Ah, where A is the area of the base polygon and h is the height of the pyramid.
To find the height of the pyramid, we can use the Pythagorean theorem. Let's say the side length of the base polygon is s, and the apothem (the distance from the center of the polygon to the midpoint of a side) is a. Then the height of the pyramid is given by h = sqrt(s^2 - a^2).
Here's the Python code to compute the volume of a regular polygon inscribed in a pyramid, given the number of sides and the side length:
main.py346 chars17 lines
We can then call this function with the number of sides and the side length:
main.py81 chars5 lines
This will output the volume of the pyramid with a regular pentagon inscribed in the base.
gistlibby LogSnag