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

To find the surface area of a regular polygon circumscribed around a triangular prism in C#, we first need to find the side length of the regular polygon.

main.cs
double apothem = (height / 2) / Math.Tan(Math.PI / n); // where n is the number of sides
double sideLength = (2 * apothem) * Math.Tan(Math.PI / n);
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Once we have the side length, we can find the surface area of one of the faces of the regular polygon:

main.cs
double faceArea = (n * Math.Pow(sideLength, 2)) / (4 * Math.Tan(Math.PI / n));
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Since the triangular prism has two triangular faces and n rectangular faces, the total surface area would be:

main.cs
double triangleArea = (baseLength * height) / 2;
double totalArea = (n * faceArea) + (2 * triangleArea);
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Where baseLength is the length of one of the sides of the base triangle of the prism, and height is the height of the prism.

And that's how you can find the surface area of a regular polygon circumscribed around a triangular prism in C#!