find the surface area of a regular polygon inscribed in a sphere in csharp

To find the surface area of a regular polygon inscribed in a sphere, we can use the following formula:

Surface Area = Number of Faces * Area of Each Face

where:

Number of Faces = number of sides of the polygon Area of Each Face = area of a triangle with vertices at the center of the sphere and two adjacent vertices of the polygon

Here's the code in C#:

using System;

class Program
{
    static void Main(string[] args)
    {
        int n = 6; // number of sides of the polygon
        double r = 5; // radius of the sphere

        // calculate the side length of the polygon
        double a = 2 * r * Math.Sin(Math.PI / n);

        // calculate the area of each face
        double area = 0.5 * a * r;

        // calculate the surface area of the polygon
        double surfaceArea = n * area;

        Console.WriteLine($"Surface area of the {n}-sided polygon inscribed in a sphere with radius {r} is {surfaceArea}");
    }
}
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In this example, we assume that the polygon has 6 sides and the radius of the sphere is 5. We calculate the side length of the polygon using the formula a = 2 * r * sin(pi/n), where n is the number of sides and pi is the value of pi (approximately 3.14159). Then, we calculate the area of each face using the formula area = 0.5 * a * r. Finally, we calculate the surface area of the polygon by multiplying the number of faces by the area of each face. The output of the program is:

main.cs
Surface area of the 6-sided polygon inscribed in a sphere with radius 5 is 156.15242310424423
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