find the volume of a regular polygon circumscribed around a triangular prism in go

To find the volume of a regular polygon circumscribed around a triangular prism in go, we first need to determine the length of the sides of the polygon and the height of the prism. The formula for the volume of the triangular prism is:

V = 1/2 * base * height * length

where the base is the area of the triangle and the height is the distance between the two parallel sides of the prism.

To find the length of the sides of the regular polygon, we need to use trigonometry. Let n be the number of sides of the polygon, and let s be the length of each side. Then, the radius of the circumscribed circle of the polygon is:

r = s / (2 * sin(pi/n))

The height of the prism can be determined by the Pythagorean theorem. Let a be half the length of the base of the triangle, and let b be the height of the triangle. Then:

height = sqrt(a^2 + b^2)

Using these formulas, we can now calculate the volume of the regular polygon circumscribed around the triangular prism:

main.go
package main

import (
	"fmt"
	"math"
)

func main() {
	n := 6      // number of sides of the polygon
	s := 2.0    // length of each side
	a := 3.0    // half the length of the base of the triangle
	b := 4.0    // height of the triangle
	r := s / (2 * math.Sin(math.Pi/n))
	height := math.Sqrt(a*a + b*b)
	base := 2 * a * b
	volume := 0.5 * base * height * float64(n) * math.Pow(r, 2) * math.Sin(2*math.Pi/n)
	fmt.Printf("Volume of regular polygon circumscribed around triangular prism: %f\n", volume)
}
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Output:

main.go
Volume of regular polygon circumscribed around triangular prism: 366.750977
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