find the volume of a regular polygon inscribed in a pyramid in go

To find the volume of a regular polygon inscribed in a pyramid, we need to know the area of the base of the pyramid and the height of the pyramid.

Here's the formula to calculate the volume:

main.go
V = (1/3) * A * h
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where:

• V = Volume of the pyramid
• A = Area of the base
• h = Height of the pyramid

To calculate the area of the base of a regular polygon, we first need to know the length of one of its sides, which we can find using the formula:

main.go
s = 2 * r * sin(pi/n)
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where:

• s = length of one side of the polygon
• r = radius of the polygon (distance from center to a vertex)
• n = number of sides of the polygon
• pi = 3.14159...

Once we have the length of one side of the polygon, we can calculate its area using the formula:

main.go
A = (n * s^2) / (4 * tan(pi/n))
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where:

• A = Area of the polygon
• s = length of one side of the polygon
• n = number of sides of the polygon
• pi = 3.14159...

Putting it all together, here's the code in Go:

main.go
package main

import (
	"fmt"
	"math"
)

func main() {
	// Parameters
	n := 6        // number of sides of the polygon
	r := 5.0      // radius of the polygon (distance from center to a vertex)
	h := 12.0     // height of the pyramid
	pi := math.Pi // 3.14159...

	// Calculate length of one side of the polygon
	s := 2 * r * math.Sin(pi/float64(n))

	// Calculate area of the polygon
	A := (float64(n) * math.Pow(s, 2)) / (4 * math.Tan(pi/float64(n)))

	// Calculate volume of the pyramid
	V := (1.0 / 3.0) * A * h

	// Print results
	fmt.Printf("Number of sides: %v\n", n)
	fmt.Printf("Radius: %v\n", r)
	fmt.Printf("Height: %v\n", h)
	fmt.Printf("Length of one side of polygon: %v\n", s)
	fmt.Printf("Area of polygon: %v\n", A)
	fmt.Printf("Volume of pyramid: %v\n", V)
}
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Note: Replace the values of n, r, and h with your own values to find the volume of a regular polygon inscribed in a pyramid.