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

To find the volume of a regular polygon inscribed in a pyramid, we can use the formula:

V = (1/3) * A_base * h

where A_base is the area of the base of the pyramid and h is the height of the pyramid.

To find the area of the base, we need to calculate the perimeter of the regular polygon inscribed in it. We can use the following formula for the perimeter of a regular polygon:

P = n * s

where n is the number of sides and s is the length of each side.

The length of each side can be calculated using the radius of the inscribed circle and the sine function:

s = 2 * r * sin(pi/n)

where pi is the mathematical constant pi and n is the number of sides.

Now, we can find the area of the base using the following formula:

A_base = (1/2) * P * apothem

where apothem is the distance from the center of the base to the midpoint of a side.

Finally, we can calculate the height of the pyramid using the Pythagorean theorem:

h = sqrt(r^2 - apothem^2)

Putting it all together, we get the following code:

main.rb
def inscribed_polygon_pyramid_volume(n, r, h)
  # Calculate side length
  s = 2 * r * Math.sin(Math::PI/n)
  
  # Calculate perimeter
  p = n * s
  
  # Calculate apothem
  ap = r * Math.cos(Math::PI/n)
  
  # Calculate base area
  base_area = (1.0/2) * p * ap
  
  # Calculate volume
  volume = (1.0/3) * base_area * h
  
  return volume
end
343 chars
19 lines

We can then call this function with the number of sides (n), the radius of the inscribed circle (r), and the height of the pyramid (h) to find the volume of the regular polygon inscribed in the pyramid.