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

To find the surface area of a regular polygon circumscribed around a cylinder, we need to first find the circumference and height of the cylinder. Then, we can use those values to calculate the surface area of the polygon.

Assuming we have the radius of the cylinder and the number of sides of the polygon, we can use the following TypeScript code to find the surface area:

index.ts
function surfaceAreaOfCircumscribedPolygon(radius: number, sides: number): number {
  const height = radius * 2;
  const circumference = 2 * Math.PI * radius;
  const apothem = radius * Math.cos(Math.PI / sides);
  const sideLength = 2 * apothem * Math.tan(Math.PI / sides);

  const polygonSurfaceArea = sides * sideLength * height;
  const curvedSurfaceArea = circumference * height;

  return polygonSurfaceArea + curvedSurfaceArea;
}
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This function first calculates the height of the cylinder by multiplying the radius by 2. Then, it calculates the circumference of the base of the cylinder using the formula circumference = 2 * pi * radius.

Next, it calculates the apothem (i.e., the distance from the center of the polygon to the midpoint of a side) of the circumscribed polygon using the formula apothem = radius * cos(pi / sides). It also calculates the length of a side of the polygon using the formula sideLength = 2 * apothem * tan(pi / sides).

Using these values, the function calculates the surface area of the polygon by multiplying the number of sides by the length of a side by the height of the cylinder. It also calculates the curved surface area of the cylinder by multiplying the circumference by the height.

Finally, the function returns the sum of the polygon surface area and the curved surface area.

Example usage:

index.ts
const radius = 5;
const sides = 6;
const surfaceArea = surfaceAreaOfCircumscribedPolygon(radius, sides);

console.log(`Surface area of ${sides}-sided polygon circumscribed around cylinder with radius ${radius}: ${surfaceArea}`);
// Output: Surface area of 6-sided polygon circumscribed around cylinder with radius 5: 515.314917034732
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In this example, we calculate the surface area of a regular hexagon circumscribed around a cylinder with a radius of 5 units. The output is approximately 515.31 square units.