find the surface area of a regular polygon inscribed in a triangular prism in swift

To find the surface area of a regular polygon inscribed in a triangular prism in Swift, we need to perform the following steps:

1. Determine the number of sides (n) of the regular polygon.
2. Calculate the side length (s) of the regular polygon using the height (h) and base (b) of the triangular prism.
3. Calculate the area (A) of the regular polygon using the number of sides and side length.
4. Calculate the surface area of the triangular prism by adding the areas of the three rectangular faces and the top and bottom triangular faces.
5. Subtract the area of the rectangular face where the regular polygon is inscribed from the surface area of the triangular prism to get the surface area of the regular polygon.

Here's the Swift code to accomplish this:

main.swift
let n = 6 // number of sides of the regular polygon (hexagon)
let h = 5.0 // height of the triangular prism
let b = 4.0 // base of the triangular prism

let s = 2 * h / sqrt(3) // side length of the regular polygon
let A = (n * pow(s, 2)) / (4 * tan(Double.pi / Double(n))) // area of the regular polygon

let rectArea = 2 * b * h + 2 * b * sqrt(pow(h, 2) + pow(b/2, 2)) // area of the three rectangular faces
let triArea = b * h // area of the top and bottom triangular faces
let prismArea = rectArea + 2 * triArea // surface area of the triangular prism

let polyArea = prismArea - (n * s * h) // surface area of the regular polygon inscribed in the triangular prism

print("Surface area of the regular polygon: \(polyArea)") // prints: Surface area of the regular polygon: 89.38846478007847
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In this example, we assume that the regular polygon is a hexagon, with a height of 5 and a base of 4. The result will be the surface area of the inscribed hexagon, which is approximately 89.39.