A polygon has an area of 225 square meters. If the area is tripled, how does each side length change?

Let me tell you the process so that you get to the answer

Remember first that the area of a regular polygon with x sides has each of them a length which can be represented by y

A = 1/4 * xy^2 * Cot (180/x)

The purpose is to solve for y, so we get

y^2 = 4A / (xCot (180/x))

y = √ (4A / (xCot (180/x)))

The thing we need to change is A in the previous formula and with that we can use the equaation to be a constant. This could be represented by Z

Z = √ (4 / (xCot (180/x)))

so

Y = Z√A

If we increase area by a factor s, y increases by a factor of √x.

So if you want to know the triple then you need to increase it by √3