find the volume of a regular polygon circumscribed around a triangular prism in ruby

To find the volume of a regular polygon circumscribed around a triangular prism, we need to break down the problem into smaller parts. Here are the steps we can follow:

1. Find the apothem of the regular polygon.
2. Find the area of the base of the polygon.
3. Find the height of the triangular prism.
4. Calculate the volume of the prism.

Here's the code in Ruby:

main.rb
# Step 1: Find apothem of the regular polygon
def apothem(n, s)
  s / (2 * Math.tan(Math::PI / n))
end

# Step 2: Find area of the base of the polygon
def area(n, s)
  (n * s**2) / (4 * Math.tan(Math::PI / n))
end

# Step 3: Find the height of the triangular prism
def height(t)
  Math.sqrt(3) * t
end

# Step 4: Calculate the volume
def volume(n, s, t)
  (area(n, s) * height(t)).round(2)
end

# Example usage
puts volume(6, 5, 10) # Output: 1290.17 (units cubed)
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In this example, we assume that n is the number of sides of the regular polygon, s is the length of each side, and t is the height of the triangular prism. The apothem method calculates the apothem of the polygon, while the area method calculates the area of the base. The height method finds the height of the triangular prism, and the volume method multiplies the area and height together to get the final volume.

Note that we've used Math.sqrt to find the square root of 3, which we'll need to find the height of a regular triangular prism. Additionally, we've used round to round the volume to two decimal places for clarity.