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

To find the surface area of a regular polygon circumscribed around a cone, we first need to find the slant height of the cone. Once we have the slant height, we can use trigonometry to find the height of the cone and the radius of the base of the cone. With the height and radius, we can then find the perimeter and apothem of the regular polygon. Finally, we can use the formula for the surface area of a polygon to find the surface area of the regular polygon.

Here's the code to do all of that in Swift:

main.swift
// Define the number of sides of the regular polygon and the radius of the circumscribed circle
let n = 6 // change this to the number of sides you want
let r = 5.0 // change this to the radius of the circle you want

// Find the slant height of the cone
let slantHeight = sqrt(pow(r, 2) + pow((r * cos(Double.pi / Double(n))), 2))

// Find the height of the cone
let height = slantHeight - r

// Find the radius of the base of the cone
let baseRadius = r * sin(Double.pi / Double(n))

// Find the perimeter and apothem of the regular polygon
let perimeter = 2 * n * baseRadius
let apothem = baseRadius * cos(Double.pi / Double(n))

// Find the surface area of the regular polygon
let surfaceArea = perimeter * slantHeight + (n * baseRadius * apothem)
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Note: In this code, we assume that the regular polygon is inscribed in a circle with a radius of 'r'. If your problem specifies a different circle, you may need to adjust the code accordingly.

gistlibby LogSnag