Solution: The original side length of the square is $ \frac404 = 10 \, \textcm $. The original area is $ 10^2 = 100 \, \textcm^2 $. After increasing each side by $ 2 \, \textcm $, the new side length is $ 12 \, \textcm $, and the new area is $ 12^2 = 144 \, \textcm^2 $. The increase in area is $ 144 - 100 = 44 \, \textcm^2 $. - Crosslake