The length of a rectangle is decreased by 20% while the breadth is increased by 20%. Then the area of the rectangle will

Let the original length be $L$ and the original breadth be $B$. The original area is:
$$A=L\times B$$

Following the adjustments:

* New length ($L^{\prime }$) = $L-0.20L=0.80L$
* New breadth ($B^{\prime }$) = $B+0.20B=1.20B$

The new area ($A^{\prime }$) becomes:

$$A^{\prime }=L^{\prime }\times B^{\prime }=(0.80L)\times (1.20B)=0.96(L\times B)=0.96A$$

The percentage change in area is calculated as:

$$\text{Percentage Change}=\frac{A^{\prime }-A}{A}\times 100\%=\frac{0.96A-A}{A}\times 100\%=-0.04\times 100\%=-4\%$$

The negative sign indicates that the area decreases by $4\%$.