ideal_polygon.rb

require 'matrix'
# A polygon that's most likely to be encountured in nature.
# These are normally convex and concave polygons.
# (all sides and all angles are not congruent)
class IdealPolygon
  attr_accessor :coordinates, :number_of_sides

  def initialize(coordinates=[])
    @coordinates = coordinates
  end

  # The coordinates (x1,y1), (x2,y2), ..., (xN,yN) of a convex polygon
  # need to me arranged in the "determinant". The coordinates must be taken
  # in clockwise order around the polygon, beginning and ending at the same point.
  def area
    Matrix[*self.coordinates].determinate
  end

  def number_of_sides
    @number_of_sides ||= (self.coordinates.count / 2)
  end
end

regular_polygon.rb

# A polygon class for which all sides and all angles are congruent
class RegularPolygon
  attr_accessor :number_of_sides, :length_of_a_side, :inscribed_radius, :circumcircle_radius

  def initialize(number_of_sides=0.0, length_of_a_side=0.0, inscribed_radius=0.0, circumcircle_radius=0.0)
    @number_of_sides     = number_of_sides
    @length_of_a_side    = length_of_a_side
    @inscribed_radius    = inscribed_radius.nonzero? || self.apothem
    @circumcircle_radius = circumcircle_radius
  end

  # This is just the algorithm to find the inscribed_radius
  def apothem
    0.5 * self.length_of_a_side * Math.cot(108/self.number_of_sides)
  end

  def area
    0.5 * self.number_of_sides * self.length_of_a_side * self.inscribed_radius
  end
end