find the volume of a regular polygon inscribed in a pyramid in typescript

To calculate the volume of a regular polygon inscribed in a pyramid in TypeScript, we need to know the side length of the polygon, the apothem (the distance from the center of the polygon to the midpoint of a side), and the height of the pyramid.

We can start by defining a function that calculates the area of a regular polygon given its side length and number of sides. We can then use the apothem and area to calculate the volume of the pyramid.

Here's the TypeScript code:

index.ts
function areaRegularPolygon(sideLength: number, numSides: number): number {
  const denominator = 4 * Math.tan(Math.PI / numSides);
  return (sideLength ** 2 * numSides) / denominator;
}

function volumeRegularPolygonPyramid(sideLength: number, numSides: number, height: number): number {
  const baseArea = areaRegularPolygon(sideLength, numSides);
  const apothem = sideLength / (2 * Math.tan(Math.PI / numSides));
  return (1/3) * baseArea * height;
}

// Example usage
const sideLength = 5;
const numSides = 6;
const height = 10;
const volume = volumeRegularPolygonPyramid(sideLength, numSides, height);
console.log(`The volume of a regular ${numSides}-sided polygon inscribed in a pyramid with height ${height} and side length ${sideLength} is ${volume}`);
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In this code, we first define the areaRegularPolygon function that takes the side length and number of sides and returns the area of the polygon. We use the formula:

area = (sideLength^2 * numSides) / (4 * tan(pi/numSides))

where pi is the mathematical constant pi.

We then define the volumeRegularPolygonPyramid function that takes the side length, number of sides, and height of the pyramid and returns the volume. We use the formula:

volume = (1/3) * baseArea * height

where baseArea is the area of the regular polygon base of the pyramid.

We test the functions by calculating the volume of a regular hexagon inscribed in a pyramid with a height of 10 units and a side length of 5 units. The result is printed to the console.