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

To find the surface area of a regular polygon circumscribed around a pyramid, we first need to find the slant height and apothem of the pyramid. Then we can use the formula for the surface area of a regular pyramid:

Surface area = 1/2 * Perimeter * slant height + Base area

Here's the C# code to calculate the surface area of a regular polygon circumscribed around a pyramid:

main.cs
using System;

namespace Geometry
{
    class Program
    {
        static void Main(string[] args)
        {
            double sideLength = 5.0; // Length of the side of the polygon
            int numSides = 6; // Number of sides of the polygon
            double height = 10.0; // Height of the pyramid

            double apothem = sideLength / (2 * Math.Tan(Math.PI / numSides));
            double slantHeight = Math.Sqrt(Math.Pow(height, 2) + Math.Pow(apothem, 2));
            double perimeter = numSides * sideLength;
            double baseArea = (numSides * Math.Pow(sideLength, 2)) / (4 * Math.Tan(Math.PI / numSides));
            double surfaceArea = 0.5 * perimeter * slantHeight + baseArea;

            Console.WriteLine("Surface Area: " + surfaceArea);
        }
    }
}
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Note that we use Math.Tan() and Math.PI to calculate the apothem and base area of the polygon, and we use the Pythagorean theorem to calculate the slant height.

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