find the area of a regular polygon inscribed in a circle in ruby

Here's a Ruby function that takes the number of sides of a regular polygon and the radius of its inscribing circle as arguments, and returns the area of the polygon:

main.rb
def area_of_polygon(num_sides, radius)
  apothem = radius * Math.cos(Math::PI / num_sides)
  length_of_side = 2 * radius * Math.sin(Math::PI / num_sides)
  area = 0.5 * num_sides * length_of_side * apothem
end
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The formula for the area of a regular polygon is:

main.rb
area = 0.5 * num_sides * length_of_side * apothem
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where num_sides is the number of sides of the polygon, length_of_side is the length of each side, and apothem is the distance from the center of the polygon to the midpoint of a side.

To calculate apothem and length_of_side, we can use the following formulas:

main.rb
apothem = radius * cos(pi / num_sides)

length_of_side = 2 * radius * sin(pi / num_sides)
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where radius is the radius of the inscribed circle of the polygon, and pi is the mathematical constant.

Thus, the function uses the above formulas to compute apothem and length_of_side, plugs them into the formula for the area, and returns the result.