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

To find the surface area of a regular polygon circumscribed around a pyramid in Ruby, we need to follow a few steps:

Find the apothem (i.e., the perpendicular distance from the center of the polygon to one of its sides).
Find the slant height of the pyramid (i.e., the distance from the apex to the center of one of the polygon's sides).
Find the perimeter of the polygon.
Use these values to calculate the surface area of the pyramid.

Here's the Ruby code:


main.rb
# Define the number of sides and the length of each side of the polygon
num_sides = 6
side_length = 5

# Calculate the apothem of the polygon
apothem = side_length / (2 * Math.tan(Math::PI/num_sides))

# Calculate the slant height of the pyramid
slant_height = Math.sqrt(apothem**2 + side_length**2)

# Calculate the perimeter of the polygon
perimeter = num_sides * side_length

# Calculate the base area of the pyramid
base_area = (num_sides * side_length * apothem) / 2

# Calculate the lateral area of the pyramid
lateral_area = (perimeter * slant_height) / 2

# Calculate the total surface area of the pyramid
total_surface_area = base_area + lateral_area

puts "The surface area of the pyramid is #{total_surface_area} units squared."
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In the code above, we assume that the polygon is a regular hexagon (i.e., num_sides = 6) and that each side has length 5. However, you can change these values to fit your specific use case.

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