The sides of square M are half as long as the sides of square N. What is the ratio of the area of square M to the area of square N?
x = y / 2
x^2 = y^2 / 4
think about it. Since each side of N is twice as long as that of M,
(area M)/(area N) = (m*m)/(2m*2m) = m^2/4m^2 = 1/4
area grows as the square of the linear scale, since it involve two linear dimensions.