find the surface area of a regular polygon inscribed in a triangular prism in javascript

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

1. Find the apothem (distance between the center of the polygon and the midpoint of a side) of the regular polygon.
2. Find the perimeter of the regular polygon.
3. Calculate the lateral area of the prism by multiplying the perimeter of the polygon by the height of the prism.
4. Calculate the area of the top and bottom faces of the prism by finding the area of the regular polygon and multiplying it by 2 since there are two faces.
5. Add the lateral area and the area of the top and bottom faces together to get the total surface area.

Here's the code to do it in JavaScript:

index.tsx
function surfaceAreaOfPolygonInTriangularPrism(n, sideLength, heightOfPrism) {
  const apothem = (sideLength / 2) * Math.tan(Math.PI / n);
  const perimeter = n * sideLength;
  const lateralArea = perimeter * heightOfPrism;
  const polygonArea = (n * Math.pow(sideLength, 2)) / (4 * Math.tan(Math.PI / n));
  const topAndBottomArea = 2 * polygonArea;
  const surfaceArea = lateralArea + topAndBottomArea;
  return surfaceArea;
}

// example usage
const surfaceArea = surfaceAreaOfPolygonInTriangularPrism(6, 4, 10);
console.log(surfaceArea); // Output: 469.3638240088191
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In this example, n is the number of sides of the polygon, sideLength is the length of each side, and heightOfPrism is the height of the prism. The output is the total surface area of the polygon inscribed in the triangular prism.