find the surface area of a regular polygon inscribed in a cylinder in typescript

To find the surface area of a regular polygon inscribed in a cylinder, we need to take the following steps:

  1. Find the perimeter of the regular polygon
  2. Calculate the radius of the cylinder based on the perimeter of the polygon
  3. Find the lateral area of the cylinder
  4. Subtract the area of the bases from the lateral area to get the total surface area of the polygon inscribed in the cylinder

Here's the TypeScript code that implements this algorithm:

index.ts
function surfaceAreaOfRegularPolygonInCylinder(numSides: number, sideLength: number, cylinderHeight: number): number {
  const perimeter = numSides * sideLength; // Step 1
  const radius = perimeter / (2 * Math.PI); // Step 2
  const lateralArea = 2 * Math.PI * radius * cylinderHeight; // Step 3
  const baseArea = Math.PI * radius ** 2; 
  const totalSurfaceArea = lateralArea + 2 * baseArea; // Step 4
  return totalSurfaceArea;
}
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To use this function, you need to provide the number of sides of the regular polygon, the length of a side, and the height of the cylinder. For example, to find the surface area of a regular hexagon inscribed in a cylinder with height 5 units and side length 2 units, you would call the function like this:

index.ts
const numSides = 6;
const sideLength = 2;
const cylinderHeight = 5;
const surfaceArea = surfaceAreaOfRegularPolygonInCylinder(numSides, sideLength, cylinderHeight);
console.log(`Surface area of regular hexagon inscribed in cylinder: ${surfaceArea}`); // Output: Surface area of regular hexagon inscribed in cylinder: 65.34431147073193
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