what happens to the surface area of an object when enlarged

what happens to the surface area of an object when enlarged

Think about it this way....area is just a function of some "width" times some "length"

Now suppose that I have 1 "square foot" of area. That would be a square with one side = 1 foot

Now suppose that I doubled the length of each side ( a scaling factor of 2)....I would have 2ft X 2ft = 4 square feet of "area"......4 times as much.

Now suppose that, instead of doubling each side, I tripled it ( a scaling factor of 3)....I would have 3ft X 3ft = 9 square feet of "area"......9 times as much

Again, suppose that, instead of doubling each side, I quadrupled it (a scaling factor of 4)....I would have 4ft X 4ft = 16 square feet of "area"......16 times as much

This leads us to believe that each suare foot of the surface of an object would behave the very same way.

Thus, the surface area increases by (n²) times when we enlarge it by some scaling factor  "n" ...(Note that n needn't be an integer....it could be anything > 1.)

I hope that helps......