This is because the percentage increase in the area of a square is given by:

\(\text{Percentage increase} = \frac{\text{New area} - \text{Old area}}{\text{Old area}} \times 100\%\)

The old area of the square is given by:

\(\text{Old area} = (\text{Old side})^2 = (20 \text{ cm})^2 = 400 \text{ cm}^2\)

The new area of the square is given by:

\(\text{New area} = (\text{New side})^2 = (21 \text{ cm})^2 = 441 \text{ cm}^2\)

Substituting these values into the formula, we get:

\(\text{Percentage increase} = \frac{441 - 400}{400} \times 100\%\)

\(\text{Percentage increase} = \frac{41}{400} \times 100\%\)\(\text{Percentage increase} =0.1025 \times 100\%\)\(\text{Percentage increase} = 10.25\%\)

Therefore, the percentage increase in the area of the square is 10.25%.