find the surface area of a regular polygon circumscribed around a pyramid in go

To find the surface area of a regular polygon that is circumscribed around a pyramid, we need to find the area of each triangular face of the pyramid and the area of the regular polygon base.

Here's an implementation in Go:

main.go
package main

import (
    "fmt"
    "math"
)

func main() {
    // Number of sides of the regular polygon
    n := 6
    
    // Length of each side of the polygon
    a := 5.0
    
    // Height of the pyramid
    h := 10.0
    
    // Apothem of the polygon
    apothem := a / (2 * math.Tan(math.Pi/float64(n)))
    
    // Circumradius of the polygon
    circumradius := a / (2 * math.Sin(math.Pi/float64(n)))
    
    // Area of the regular polygon base
    polygonArea := 0.5 * float64(n) * a * apothem
    
    // Area of each triangular face of the pyramid
    faceArea := 0.5 * a * h
    
    // Surface area of the pyramid
    surfaceArea := polygonArea + (float64(n) * faceArea)
    
    fmt.Println("Surface area of the pyramid:", surfaceArea)
}
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In this implementation, we first calculate the apothem and circumradius of the regular polygon using the number of sides and length of each side. We then use these values to calculate the area of the regular polygon base.

Next, we calculate the area of each triangular face of the pyramid by multiplying the length of each side of the polygon with the height of the pyramid and dividing by 2.

Finally, we add the area of the regular polygon base to the total area of all the triangular faces to get the surface area of the pyramid.

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