find the volume of a regular polygon inscribed in a triangular prism in ruby

We can find the volume of the regular polygon inscribed in a triangular prism by breaking down the problem into three steps:

  1. Find the height of the regular polygon. This can be done by using the Pythagorean theorem to find the length of the altitude of the triangular prism that intersects the base of the regular polygon.

  2. Find the area of the base of the regular polygon. This can be done using the formula for the area of a regular polygon:

    main.rb
                area = (n * s^2) / (4 * tan(pi/n))
    
    47 chars
    2 lines

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

  3. Find the volume of the regular polygon by multiplying the area of the base by the height calculated in step 1.

Here's the Ruby code that implements this algorithm:

main.rb
def regular_polygon_inscribed_in_triangular_prism(num_sides, side_length, base_width, height)
  # Step 1: calculate the height of the regular polygon
  h = Math.sqrt(height**2 - base_width**2 / 4)

  # Step 2: calculate the area of the base of the regular polygon
  area = (num_sides * side_length**2) / (4 * Math.tan(Math::PI/num_sides))

  # Step 3: calculate the volume of the regular polygon
  volume = area * h

  # return the result
  return volume
end

# Example Usage:
# Find the volume of a regular hexagon inscribed in a triangular prism
num_sides = 6
side_length = 5
base_width = 10
height = 15
result = regular_polygon_inscribed_in_triangular_prism(num_sides, side_length, base_width, height)

puts "The volume of the regular polygon inscribed in the triangular prism is #{result} units cubed."
807 chars
24 lines

In this example, the output will be:

main.rb
The volume of the regular polygon inscribed in the triangular prism is 304.1247694813834 units cubed.
102 chars
2 lines

gistlibby LogSnag