If the length of a rectangle is increased by $30\%$ and width by $20\%$, its area will be increased by:

The net percentage change in area due to successive changes of $a\%$ and $b\%$ in length and width respectively can be calculated using the successive percentage formula:
$$\text{Net Increase}=\left(a+b+\frac{a\times b}{100}\right)\%$$

Given $a=30$ and $b=20$:

$$\text{Net Increase}=\left(30+20+\frac{30\times 20}{100}\right)\%$$

$$\text{Net Increase}=50+\frac{600}{100}=50+6=56\%$$