If the side of a square is increased by$25\%$, then its area is increased by how many percent?

The correct option is C 56.25%

Let the side be 10 cm. Then the area will be $100c{m}^2$

New side $=125\%of10=12.5cm;$

$Area=(12.5{)}^2=156.25$

Percentage increase in area $=56.25\%.$

Alternatively: If x is the percentage increase in the side of a square, then increase in area is given by

$x+x+\frac{x\times x}{100}=2x+\frac{x^2}{100}=25+25+\frac{25\times 25}{100}=56.25\%$