find the surface area of a regular polygon inscribed in a cone in ruby

main.rb
# Inputs
num_sides = 6   # number of sides of regular polygon
radius = 5      # radius of base of cone
height = 10     # height of cone

# Calculate side length and apothem of polygon
side_length = 2 * radius * Math.sin(Math::PI / num_sides)
apothem = radius * Math.cos(Math::PI / num_sides)

# Calculate area of each face of polygon
face_area = 0.5 * side_length * apothem

# Calculate surface area of polygon (and cone)
polygon_area = num_sides * face_area
cone_area = Math::PI * radius * (radius + Math.sqrt(height**2 + radius**2))

# Output result
puts "Surface area of regular polygon in cone: #{polygon_area} square units"
puts "Surface area of cone: #{cone_area} square units"
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