find the area of a regular polygon circumscribed around a circle in ruby

To find the area of a regular polygon circumscribed around a circle, we can use the formula:

area = 0.5 * perimeter * apothem

where perimeter is the perimeter of the polygon and apothem is the distance from the center of the polygon to the midpoint of a side.

In this case, we can calculate perimeter by multiplying the number of sides by the length of a side. We can calculate the length of a side using the radius of the circumscribed circle and the trigonometric functions sine and cosine.

Here's the code to calculate the area of a regular polygon circumscribed around a circle in Ruby:

main.rb
def polygon_area(num_sides, radius)
  side_length = 2 * radius * Math.sin(Math::PI / num_sides)
  perimeter = num_sides * side_length
  apothem = radius * Math.cos(Math::PI / num_sides)
  0.5 * perimeter * apothem
end

# Example usage
num_sides = 6
radius = 5
area = polygon_area(num_sides, radius)
puts "The area of a regular polygon with #{num_sides} sides circumscribed around a circle with radius #{radius} is #{area}."
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Output:

main.rb
The area of a regular polygon with 6 sides circumscribed around a circle with radius 5 is 64.9519052838329.
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