find the surface area of a regular polygon inscribed in a cone in swift

To find the surface area of a regular polygon inscribed in a cone, we need to first find the slant height and the base perimeter of the cone. Here's the code to find the surface area in Swift:

main.swift
// assume coneHeight, coneRadius, and numSides (number of sides of polygon) are given

let slantHeight = sqrt(coneHeight * coneHeight + coneRadius * coneRadius)
let basePerimeter = 2 * Double.pi * coneRadius
let sideLength = basePerimeter / Double(numSides)
let apothemLength = coneRadius * cos(Double.pi / Double(numSides))
let polygonArea = 0.5 * apothemLength * sideLength * Double(numSides)
let baseArea = Double.pi * coneRadius * coneRadius
let surfaceArea = polygonArea + baseArea
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In the code above, we first calculate the slant height and the base perimeter of the cone using the given height and radius. Then we calculate the side length and apothem length of the inscribed polygon using the base perimeter and number of sides.

Finally, we calculate the area of the polygon using the side length and apothem length, and add it to the base area of the cone to get the total surface area of the cone and inscribed polygon.