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

To find the surface area of a regular polygon inscribed in a cylinder, we need to calculate the area of the polygon and the area of the cylinder that is not covered by the polygon.

To calculate the area of the polygon:

1. Find the length of one side of the polygon. Let's call this 'a'.
2. Find the number of sides of the polygon. Let's call this 'n'.
3. Calculate the radius of the inscribed circle. Let's call this 'r' and it can be found using r = a/2sin(π/n).
4. Calculate the area of the polygon. Let's call this 'A_p' and it can be found using A_p = 0.5n(a*r).

To calculate the area of the cylinder that is not covered by the polygon:

1. Calculate the height of the cylinder. Let's call this 'h'.
2. Calculate the circumference of the inscribed circle. Let's call this 'c' and it can be found using c = 2πr.
3. Calculate the area of the cylinder. Let's call this 'A_c' and it can be found using A_c = 2πrh - nar.

Putting it all together, the total surface area can be found using S = A_p + A_c.

Here's the javascript code to implement this:

index.tsx
function surfaceAreaOfPolygonInCylinder(a, n, h) {
  const r = a / (2 * Math.sin(Math.PI / n));
  const A_p = 0.5 * n * a * r;
  const c = 2 * Math.PI * r;
  const A_c = 2 * Math.PI * r * h - n * a * r;
  const S = A_p + A_c;
  return S;
}

// Example usage
const surfaceArea = surfaceAreaOfPolygonInCylinder(6, 8, 10); // Regular hexagon inscribed in a cylinder with side length of 6, 8 sides, and height of 10
console.log(surfaceArea); // Returns 989.8305363772945
467 chars
13 lines

In this example, we have a regular hexagon inscribed in a cylinder with a side length of 6, 8 sides, and a height of 10. The output is approximately 989.83 units squared.