find the volume of a regular polygon inscribed in a triangular prism in swift

To find the volume of a regular polygon inscribed in a triangular prism, we need to first calculate the area of the polygon's base, and then use trigonometry to find the height of the triangular prism. Once we have these values, we can use the formula for the volume of a triangular prism to calculate it.

Here's the code in Swift:

main.swift
let n = 6 // number of sides of the regular polygon
let r = 2.0 // the radius of the inscribed circle of the polygon
let a = 2 * r * sin(Double.pi / Double(n)) // length of one side of the polygon
let b = sqrt(pow(a, 2) - pow(r, 2)) // distance from the center of the polygon to a vertex

let baseArea = (n * pow(a, 2)) / (4 * tan(Double.pi / Double(n))) // area of the polygon's base

let height = b // height of the triangular prism

let volume = baseArea * height // volume of the triangular prism
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In this code, we first define the number of sides of the regular polygon (n) and the radius of its inscribed circle (r). Using these values, we then calculate the length of one side of the polygon (a) and the distance from the center of the polygon to a vertex (b).

Next, we calculate the area of the polygon's base (baseArea) using the formula (n * a^2) / (4 * tan(pi/n)). Finally, we set the height of the triangular prism to b and calculate its volume using the formula baseArea * height.

With this code, we can quickly and easily calculate the volume of a regular polygon inscribed in a triangular prism.