10. (12 points) As shown in the figure, the side length of square $ABCD$ is $18$, $E$ is the midpoint of $CD$, and $ABFH$ is a rectangle. The areas of the two shaded triangles are equal. Therefore, the area of quadrilateral $AEFB$ is $\qquad$

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
10. (12 points) As shown in the figure, the side length of square $ABCD$ is $18$, $E$ is the midpoint of $CD$, and $ABFH$ is a rectangle. The areas of the two shaded triangles are equal. Therefore, the area of quadrilateral $AEFB$ is $\qquad$ 216.

【Solution】Solution: According to the analysis, the areas of the two shaded triangles are equal. If we add the trapezoid $HDEG$ to both, the total areas are also equal,

i.e., the area of triangle $ADE$ is equal to the area of the right trapezoid $DEFH$. The area of $S_{\triangle ADE}=9 \times 18 \div 2=81$, so the area of the right trapezoid $DEFH$ is also 81. Therefore, the height $HD=81 \times 2 \div (9+18)=6$, hence: $FC=6$, then $S_{\triangle ECF}=9 \times 6 \div 2=27$, so the area of quadrilateral $AEFB$ is $=18 \times 18-81-27=216$. Therefore, the answer is: 216