Question

if you have a square that is getting enlarged by 2, the area is enlarged by 4, right? and if it is enlarged by 4, the area it 16 times?

Answer 1

If it is enlarged by 2,the area increases by 4+4s and if enlarged by 4 area increases by 16 +8s

Answer 2

It depends what you mean by "enlarged by 2". If you mean its sides are doubled then the area= s*s becomes new_area= (2s)*(2s)= 4*s*s = 4*area
If you mean its area is doubled (it now takes twice as much paint to cover it), then its sides were scaled by sqrt(2).