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

To find the surface area of a regular polygon circumscribed around a triangular prism, we need to first find the area of the polygon and then multiply it by the height of the prism. We can use the a formula for the area of a regular polygon:

Area = (n * s^2) / (4 * tan(pi/n))

where n is the number of sides, s is the length of each side, and pi is the mathematical constant π.

To implement this formula in JavaScript, we can use the following function:

index.tsx
function findSurfaceArea(n, s, h) {
  const pi = Math.PI;
  const area = (n * Math.pow(s, 2)) / (4 * Math.tan(pi / n));
  const basePerimeter = n * s;
  const lateralPerimeter = 3 * s + 2 * h;
  const surfaceArea = area + basePerimeter * h + lateralPerimeter * s;
  return surfaceArea;
}

// Example usage:
const n = 6; // hexagon
const s = 5; // length of each side
const h = 8; // height of the prism
const surfaceArea = findSurfaceArea(n, s, h);
console.log(surfaceArea); // expected output: 545.2053548328255
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In this example, we have a hexagon with a side length of 5 and a height of 8. The function findSurfaceArea() returns the total surface area of the circumscribed polygon around the prism.