How many times will the area of a square increase if its side is doubled?

Let the original side of the square be 3. Then its new side after doubling it will be:

3 × 2 = 6 (cm).

We determine the area of the original square by the formula S = a × a, where S is the area of the figure, and is its side, we get the following value:

S1 = 3 × 3 = 9 (cm2).

Similarly, we define the area of the enlarged square:

S2 = 6 × 6 = 36 (cm2).

Now let’s find the ratio of the enlarged square to the original:

36: 9 = 4.

Answer: the area of the new square will increase by 4 times.