【Solution】Solution: $O B: O D=9: 16$ then $S_{\triangle A O B}: S_{\triangle A O D}=9: 16$, and from $S_{\triangle A O B}=54$ we get $S_{\triangle A O D}=54 \times \frac{16}{9}=96$; similarly, $S \triangle B O E=54 \times \frac{9}{16}=\frac{243}{8}$, then half the area of the rectangle $=96+54=150$, $150-\frac{243}{8}=\frac{957}{8}=119.625$;

Answer: The area of quadrilateral $O E C D$ is 119.625. Therefore, the answer is: 119.625.
11. (6 points) In the figure, in rectangle $ABCD$, the shaded part is a right triangle with an area of $54$, the length of $OD$ is 16, and the length of $OB$ is 9. What is the area of quadrilateral $OEC D$? $\qquad$ .