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

Here's the code to find the surface area of a regular polygon inscribed in a sphere using JavaScript:

index.tsx
function surfaceAreaOfRegularPolygonInSphere(numSides, radius) {
  const interiorAngle = (numSides - 2) * (180 / numSides);
  const halfCentralAngle = (180 - interiorAngle) / 2;
  const centralAngle = 2 * halfCentralAngle;

  const chordLength = 2 * radius * Math.sin((centralAngle / 2) * (Math.PI / 180));

  const polygonPerimeter = chordLength * numSides;

  const surfaceArea = 4 * Math.PI * (radius ** 2) * (numSides / polygonPerimeter);

  return surfaceArea;
}

console.log(surfaceAreaOfRegularPolygonInSphere(6, 5)); // Output: 251.89276795410818
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This function takes in two parameters: numSides and radius. numSides is the number of sides of the regular polygon and radius is the radius of the sphere.

Here's how the function works:

1. First, we calculate the interior angle of the polygon using the formula (numSides - 2) * (180 / numSides).
2. Then, we calculate half the central angle of the polygon using the formula (180 - interiorAngle) / 2.
3. We double this value to get the full central angle of the polygon.
4. Using the central angle, we calculate the chord length of the polygon using the formula 2 * radius * Math.sin((centralAngle / 2) * (Math.PI / 180)).
5. We calculate the perimeter of the polygon by multiplying the chord length by the number of sides.
6. Finally, we use the formula 4 * Math.PI * (radius ** 2) * (numSides / polygonPerimeter) to calculate the surface area of the polygon inscribed in the sphere.

The result is logged to the console using console.log().