jmc

We start by labeling everything first: First of all, we can see that $DE=8$ since we recognize a $3:4:5$ triangle in $ADE$. Also, thanks to SAS Similarity (or AA also works), we see that $△ABC\sim △ADE.$ That means that $ABC$ is also a $3:4:5$ triangle. Since $AB=9,$ that means that $AC=15$ and $BC=12.$

We find the shaded area of $BCED$ by subtracting the areas of $ABC$ and $ADE.$ The area of $ABC$ is simply $\frac{9\cdot 12}{2}=54,$ and the area of $ADE$ is $\frac{6\cdot 8}{2}=24.$ Therefore, our desired area is $54-24=\boxed{30}{\text{ cm}}^2.$