The side of the square was enlarged by 10%. By what percentage will the area of the square be increased?

Let us denote by a the length of the side of this square, expressed in centimeters.

Then the area of this square will be a cm ^ 2.

If the side of the square is increased by 10%, then the length of the side of the resulting square will be:

a + (10/100) * a = a + (1/10) * a = a + 0.1 * a = 1.1 * a cm ^ 2,

and the area of the resulting square will be (1.1 * a) ^ 2 = (1.1) ^ 2 * a ^ 2 = 1.21 * a ^ 2 cm ^ 2.

Therefore, the area of the square will increase as a percentage by:

100 * (1.21 * a ^ 2 – a ^ 2) / a ^ 2 = 100 * 0.21 * a ^ 2 / a ^ 2 = 100 * 0.21 = 21%.

Answer: 21%.