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

The net percentage change in area resulting from individual percentage changes in dimensions can be solved using the successive percentage formula:
$$\text{Net \% Change}=x+y+\frac{xy}{100}$$

Here, $x=+30\%$ (increase in length) and $y=+20\%$ (increase in width):

$$\text{Net \% Change}=30+20+\frac{30\times 20}{100}$$

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

Thus, the total area increases by exactly $56\%$.