find the surface area of a regular polygon circumscribed around a sphere in swift

To find the surface area of a regular polygon circumscribed around a sphere, we need to first calculate the length of the polygon's edges (also called the apothem) and the radius of the sphere. We can then use these values to calculate the surface area of the polygon.

Here's the Swift code to do this:

main.swift
func surfaceAreaOfPolygonCircumscribedAroundSphere(n: Int, r: Double) -> Double {
    let pi = Double.pi
    let angle = pi / Double(n)
    let apothem = r * cos(angle)
    let edgeLength = 2.0 * r * sin(angle)
    let perimeter = Double(n) * edgeLength
    let area = 0.5 * perimeter * apothem
    
    return area
}
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Here, n is the number of sides of the polygon, and r is the radius of the sphere. The function first calculates the angle between each edge of the polygon and the center of the sphere (angle). It then uses this angle to calculate the apothem (apothem) and the length of each edge (edgeLength).

Next, the function calculates the perimeter of the polygon (perimeter) and uses it along with the apothem to calculate the surface area of the polygon (area).

Finally, the function returns the surface area of the polygon.

You can call this function with the desired values of n and r to get the surface area of the regular polygon circumscribed around a sphere.