If the side of a square is increased by $30\%$ then the find the percentage increase its area.

Let side of square is ‘$x$'

From data

‘$x$’ is increased by $30\%$

The original area of square $=x\times x$

$=x^2$

$x$ is increased by $30\%=x+\frac{30}{100}x$

$=\frac{130x}{100}=\frac{13x}{10}$

The new side is  $=\frac{13x}{10}$

The new area of square $=\frac{13x}{10}\times \frac{13x}{10}$

$=\frac{169}{100}{x}^2$

$\therefore$ increase area $=\frac{169}{100}{x}^2-x^2$

$=\frac{169x^2-100x^2}{100}=\frac{69}{100}{x}^2$

$=\frac{69x^2}{\frac{100}{x^2}}\times 100=\frac{69}{100}\times 100$

$=69\%$

(or)

$30+30+\frac{30\times 30}{100}=60+9=69\%$