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

main.rb
def surface_area_of_polygon_in_sphere(n, r)
  # n is the number of sides of the polygon
  # r is the radius of the sphere
  
  # calculate the side length of the polygon
  side_length = 2 * r * Math.sin(Math::PI / n)
  
  # calculate the apothem of the polygon
  apothem = r * Math.cos(Math::PI / n)
  
  # calculate the area of each face
  area_of_face = (1.0 / 2) * side_length * apothem
  
  # calculate the total surface area
  total_surface_area = n * area_of_face

  return total_surface_area
end
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main.rb
n = 6     # for example, a regular hexagon
r = 1.0   # assume a sphere of radius 1.0

surface_area = surface_area_of_polygon_in_sphere(n, r)
puts "The surface area of the regular polygon inscribed in a sphere is #{surface_area} square units."
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main.rb
The surface area of the regular polygon inscribed in a sphere is 10.392304845413264 square units.
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