9. (15 points) As shown in the figure, two squares $A B F E$ and $C D E F$ with side lengths of 6 are combined to form rectangle $A B C D$. $G$ is the midpoint of $D E$. Connect $B G$ and it intersects $E F$ at $H$. Find the area of pentagon $C D G H F$ in the figure.
【Analysis】$G$ is the midpoint of $DE$, so $EG=6 \div 2=3$. Since $EG: AG = EH: AB$, we can find the length of $EH$. Then, using the formula for the area of a triangle, we can find the area of triangle $EHG$. Subtracting this area from the area of the square gives the area of the shaded part. According to this, solve the problem.

【Solution】Solution: $G$ is the midpoint of $DE$
$$
\begin{array}{l}
EG=6 \div 2=3 \\
EG: AG = EH: AB \\
\text{3: }(6+3)=EH: 6 \\
3: 9=EH: 6 \\
9 EH=3 \times 6 \\
\quad EH=2 \\
6 \times 6-3 \times 2 \div 2 \\
=36-3 \\
=33
\end{array}
$$

Answer: The area of the pentagon $CDGHF$ in the figure is 33.