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

To find the surface area of a regular polygon circumscribed around a triangular prism, we need to follow these steps:

1. Find the perimeter of the regular polygon.
2. Find the apothem of the regular polygon.
3. Find the height of the triangular prism.
4. Calculate the area of each triangular face of the triangular prism.
5. Calculate the area of each rectangular face of the triangular prism.
6. Add up the areas of all the faces to get the total surface area.

Here's the TypeScript code to implement this:

index.ts
function getSurfaceArea(n: number, sideLength: number, height: number) {
  const perimeter = n * sideLength;
  const apothem = (sideLength / 2) / Math.tan(Math.PI / n);
  const triangleArea = (sideLength * apothem) / 2;
  const rectangularArea = height * sideLength;
  const totalTriangularArea = 2 * triangleArea;
  const totalRectangularArea = 3 * rectangularArea;
  return totalTriangularArea + totalRectangularArea;
}

// Example usage:
const regularPolygonSurfaceArea = getSurfaceArea(6, 5, 8); // calculates surface area of a regular hexagon with side length 5 and triangular prism height 8
console.log(regularPolygonSurfaceArea); // prints 252
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In this example, we used the function getSurfaceArea to calculate the surface area of a regular hexagon circumscribed around a triangular prism with side length 5 and height 8. The result is 252.