If the length of a rectangle is increased by 20% and its width is decreased by 20%, explain whether there is any change in the area.

1. Represent the original rectangle and apply the percentage changes as multipliers.

Let the original length be $l$ and the original width be $w$.

New length $=120\%$ of $l=1.2l$.

New width $=80\%$ of $w=0.8w$.

2. Compare the new area with the original area and state the change.

Original area $=lw$.

New area $=(1.2l)(0.8w)=0.96lw$.

Since $0.96lw$ is $96\%$ of $lw$, the area is decreased by

$100\%-96\%=4\%$.