if you were to find the area of the square originally
it would lw= a
4x4= 16
so if we doubled the sides
4x2= 8 ---- they'd become 8
now find the area of the doubled square
8x8= 64
to find out the amount by which it increased, divide the new area by the old area
64/16 =4
this means that doubling the side lengths, quadruples the area