Problem 326

The area of the shaded region and the area of the unshaded region
are each equal to $18 \text{ cm}^2$.
The area of the larger square is equal to the sum of the areas of the
shaded and unshaded regions, which is $18
$\text{}$ cm}^2+18 $\text{}$ cm}^2=36 $\text{}$ cm}^2$.

Thus, the side length of the larger square is $\sqrt{36 \text{ cm}^2}=6 \text{ cm}$.