The side of the square was increased by 30%. By what percentage has its area increased.

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

Then the area of this geometric figure will be equal to a * a = a ^ 2.

If the side length of this square is increased by three tens of percent, then the side length of the resulting square will be equal to a + (30/100) * a = a + 0.3 * a = 1.3 * a, and the area of the resulting geometric figure will be equal to 1.3 * a * 1.3 * a = 1.3 * 1.3 * a ^ 2 = 1.69 * a ^ 2.

Therefore, in percentage terms, the area of the original square will increase by:

100 * (1.69 * a ^ 2 – a ^ 2) / a ^ 2 = 100 * 0.69 * a ^ 2 / a ^ 2 = 100 * 0.69 = 69%.

Answer: 69%.