How will the area of a square change if its side is increased by one point two-thirds of the time?

Let us denote by a the length of the side of this geometric figure.

Then the area S1 of this geometric figure will be:

S1 = a * a = a ^ 2.

If the side of this geometric figure is increased by one whole two-thirds of the time, then the length of the side of the resulting square will be a * (1 + 2/3) = a * (3/3 + 2/3) = a * (3 + 2) / 3 = a * 5/3 = 5a / 3.

Then the area S2 of the resulting geometric figure will be:

S2 = 5a / 3 * 5a / 3 = 25a ^ 2/9 = (25/9) * a ^ 2 = (25/9) * S1.

Therefore, the area of the original square will increase 25/9 times.

Answer: will increase 25/9 times.