find the surface area of a regular polygon circumscribed around a cone in ruby

To find the surface area of a regular polygon circumscribed around a cone, we need to calculate the area of the base of the cone and the area of the polygon surface. Here's how to do it in Ruby:

main.rb
# Define variables
r = 5 # radius of the cone base
s = 8 # number of sides of the regular polygon
h = 10 # height of the cone

# Calculate the side length of the polygon (using trigonometry)
a = 2 * r * Math.sin(Math::PI / s)

# Calculate the area of the base of the cone
base_area = Math::PI * r ** 2

# Calculate the area of one triangular surface of the polygon (using Heron's formula)
triangle_area = 0.25 * s * a ** 2 / Math.tan(Math::PI / s)

# Calculate the total surface area
total_surface_area = (s * triangle_area) + base_area

# Output the result
puts "The surface area of the polygon circumscribed around the cone is #{total_surface_area}"
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In this example, we use the Math module to calculate the sine, tangent, and pi values needed to calculate the surface area of the regular polygon circumscribed around a cone. We define the variables r, s, and h to be the radius of the cone base, the number of sides of the regular polygon, and the height of the cone, respectively. We then calculate the side length a of one of the triangles that make up the polygon, the area of the base of the cone, the area of one triangular surface of the polygon using Heron's formula, and finally, the total surface area of the polygon circumscribed around the cone.