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

To find the surface area of a regular polygon circumscribed around a cylinder, we need to calculate the area of the polygon and the area of the cylinder that is covered by the polygon.

Assuming that we know the number of sides of the polygon and the radius and height of the cylinder, we can use the following formula:

main.rb
num_sides = 6
radius = 5
height = 10

side_length = 2 * radius * Math.sin(Math::PI / num_sides)
polygon_area = 0.5 * num_sides * side_length * radius

cylinder_area = 2 * Math::PI * radius * height + 2 * Math::PI * radius**2

surface_area = polygon_area + cylinder_area
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In the above code, we first calculate the length of each side of the polygon using the formula side_length = 2 * radius * Math.sin(Math::PI / num_sides). We then use this value to calculate the area of the polygon using the formula polygon_area = 0.5 * num_sides * side_length * radius.

Next, we calculate the area of the cylinder by first finding the lateral area using 2 * Math::PI * radius * height and then the top and bottom areas using 2 * Math::PI * radius**2. We add these values to get the total area of the cylinder.

Finally, we add the areas of the polygon and cylinder to get the surface area of the regular polygon circumscribed around the cylinder.