Given that the square ABCD has 4 units length.
So the area of square ABCD is
Area = s^2
Area = 4^2
Area = 8 units squared.
Given that the square A'B'C'D' is dilated by a factor of 2. Then, the length of the side is 2*4 = 8
So the area of square A'B'C'D' is
Area = s^2
Area = 8^2
Area = 64 units squared.
Then, the ratio of the area of A'B'C'D' to the area of ABCD is
64 : 8
8 : 1
