If the dimensions of a square are increased 10%, by what percent is the area increased?

Increasing the length by 10% means we multiply the old length x by 1.1 since

100% + 10% = 1+0.1 = 1.1

Old length = x

New length = 1.1x

Old area = x*x = x^2

New area = (1.1x) * (1.1x) = (1.1*1.1) * (x*x) = 1.21x^2

So the area increases by 21%

1.21 = 1+0.21 = 100% + 21%