1. (3 points) The left figure below is the recently discovered Archimedes' "Stomachion" puzzle, dividing a square into 14 polygonal pieces: After research, experts found that these 14 pieces can be correctly drawn on a square with a side length of $12 \mathrm{~cm}$, as shown in the figure. Question: The area of the gray piece is $\qquad$ square centimeters.
【Analysis】According to the characteristics of the gray quadrilateral, reasonably divide the figure into two triangles to find the area.
【Solution】Solution: As shown in the figure, the gray part is quadrilateral $A B C D$. Connect $B D$, then $S$ quadrilateral $A B C D=S_{\triangle A B D}+S_{\triangle B C D}=\frac{1}{2} \times 6 \times 3+\frac{1}{2} \times 3 \times 2=9+3=$ 12. Therefore, the answer is: 12.