9. (5 points) In the figure, there is a square $A B C D$ with a side length of 6 cm and an isosceles right triangle $A E F$ with a hypotenuse of 8 cm, where $E$ is on the extension of $A B$. What is the area of the shaded part in the figure in square centimeters?
【Analysis】According to the problem, the sum of the area of the shaded part and the area of the right triangle equals the area of the square plus the area of triangle $B G E$. Therefore, we can first find the area of triangle $B G E$, which will allow us to find the area of the shaded part.

【Solution】Solution: According to the analysis, $B G = B E = A E - A B = 8 - 6 = 2$ (cm), so the area of triangle $B G E$ $= B G \times B E \times \frac{1}{2} = \frac{1}{2} \times 2 \times 2 = 2$ (square cm). Since triangle $A E F$ is an isosceles right triangle,

from $A E^{2} = A F^{2} + F E^{2}$, we get $A F = 4 \sqrt{2}$,
the area of the shaded part $+ \triangle A E F$'s area $=$ the area of square $A B C D$ $+ \triangle B G E$'s area
$\Rightarrow$ the area of the shaded part $=$ the area of square $A B C D$ $+ \triangle B G E$'s area $- \triangle A E F$'s area $= 6 \times 6 + 2 - 4 \sqrt{2} \times 4 \sqrt{2} \times \frac{1}{2} = 22$ (square cm),

Therefore, the answer is: 22