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

To find the surface area of a regular polygon circumscribed around a triangular prism, we need to calculate the area of the polygon and then add the areas of the rectangular sides of the prism.

Here is some Go code to do that:

main.go
package main

import (
	"fmt"
	"math"
)

func main() {
	// Define the values for the polygon and prism
	numSides := 6                                // number of sides in the regular polygon
	sideLength := 3.0                            // length of one side of the polygon
	height := 5.0                                // height of the triangular prism
	apothem := sideLength / (2 * math.Tan(math.Pi/float64(numSides))) // apothem of the polygon (distance from center to side)

	// Calculate the area of the polygon
	polygonArea := 0.5 * float64(numSides) * apothem * sideLength

	// Calculate the area of the rectangular sides of the prism
	rectangleArea := numSides * sideLength * height

	// Calculate the total surface area
	totalArea := polygonArea + rectangleArea

	// Print the result
	fmt.Printf("Surface Area: %.2f\n", totalArea)
}
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This code defines the values for the regular polygon and triangular prism, and then uses the apothem formula to calculate the apothem of the polygon. It then calculates the area of the polygon using the apothem and side length, and the area of the rectangular sides of the prism using the number of sides, side length, and height. Finally, it adds these two areas together to calculate the total surface area and prints the result.

Note that the code assumes that the polygon is circumscribed around the prism, meaning that the vertices of the polygon touch the edges of the prism.

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