find the volume of a regular polygon circumscribed around a pyramid in swift

To find the volume of a regular polygon circumscribed around a pyramid, you can use the following formula:

Volume = (B * h) / 3

where B is the area of the base of the pyramid and h is the height of the pyramid.

To find B, we need to first find the area of one of the triangular faces of the pyramid. This can be done by using the formula:

Area = (1/2) * apothem * perimeter

where apothem is the distance from the center of the polygon to the midpoint of one of its sides, and perimeter is the sum of the lengths of all the sides of the polygon.

Assuming that the pyramid is regular, each of its triangular faces will have the same area. Therefore, to find the total area of the base, we can simply multiply the area of one face by the number of faces (which is equal to the number of sides of the polygon).

Here's the Swift code to find the volume of a regular polygon circumscribed around a pyramid:

main.swift
func volumeOfPolygonCircumscribedPyramid(numSides: Int, sideLength: Float, height: Float) -> Float {
    let apothem = sideLength / (2 * tan(Float.pi / Float(numSides)))
    let perimeter = Float(numSides) * sideLength
    let baseArea = Float(numSides) * (0.5 * apothem * perimeter)
    let volume = (baseArea * height) / 3
    
    return volume
}
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To use this function, simply pass in the number of sides of the polygon, the length of each side, and the height of the pyramid as arguments. The function will return the volume of the pyramid in whatever unit of measurement you are using for the side length and height.