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

To find the surface area of a regular polygon circumscribed around a cone in TypeScript, we need to follow these steps:

1. Find the slant height of the cone.
2. Find the length of one side of the regular polygon.
3. Calculate the perimeter of the polygon.
4. Find the apothem of the polygon.
5. Calculate the lateral surface area of the cone.
6. Add the lateral surface area of the cone to the surface area of the polygon to get the total surface area.

Here's the TypeScript code that implements this algorithm:

index.ts
function surfaceAreaOfRegularPolygonCircumscribedAroundCone(numSides: number, radius: number, height: number): number {
  const slantHeight = Math.sqrt(radius ** 2 + height ** 2);
  const sideLength = 2 * radius * Math.tan(Math.PI / numSides);
  const perimeter = numSides * sideLength;
  const apothem = radius * Math.cos(Math.PI / numSides);
  const lateralArea = Math.PI * radius * slantHeight;
  const polygonArea = (perimeter * apothem) / 2;
  const totalArea = polygonArea + lateralArea;
  return totalArea;
}
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To use this function, simply call it with the number of sides of the regular polygon, the radius of the circumscribed circle, and the height of the cone, like this:

index.ts
const area = surfaceAreaOfRegularPolygonCircumscribedAroundCone(6, 5, 8);
console.log(area); // Output: 449.1980375680188
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This will calculate and log the surface area of a regular hexagon circumscribed around a cone with a radius of 5 and a height of 8.