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

index.ts
function surfaceAreaOfPyramidInscribedInRegularPolygon(numSides: number, sideLength: number, height: number): number {
  const perimeter = numSides * sideLength;
  const apothem = sideLength / (2 * Math.tan(Math.PI / numSides));
  const slantHeight = Math.sqrt(apothem ** 2 + height ** 2);
  const baseArea = (perimeter * apothem) / 2;
  const lateralArea = (perimeter * slantHeight) / 2;
  const totalSurfaceArea = baseArea + lateralArea;
  return totalSurfaceArea;
}

// Example usage
const numSides = 6; // hexagon
const sideLength = 5;
const height = 8;
const surfaceArea = surfaceAreaOfPyramidInscribedInRegularPolygon(numSides, sideLength, height);
console.log(`Surface area of pyramid circumscribed around a regular ${numSides}-gon with side length ${sideLength} and height ${height}: ${surfaceArea}`);
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