13. (12 points) The side length of a regular dodecagon is 12 cm, then the area of the shaded part in the figure is $\qquad$ square centimeters.
【Solution】Solution: As shown in the figure, it is easy to know that $\angle A D C=\frac{1}{2}\left(180^{\circ}-30^{\circ}\right)=75^{\circ}, \angle D A C=\frac{1}{2}\left(150^{\circ}-90^{\circ}\right)$
$$
\begin{array}{l}
=30^{\circ}, \\
\therefore \angle A C D=180^{\circ}-\angle A D C-\angle D A C=75^{\circ}, \\
\therefore A D=A C=12, \\
\because \angle A C B=180^{\circ}-75^{\circ}-45^{\circ}=60^{\circ}, \\
\therefore \angle A B C=30^{\circ}, \because \angle C A B=90^{\circ}, \\
\therefore B C=2 A C=24,
\end{array}
$$
$\therefore$ The area of the shaded part $=24 \times 24=576$ square centimeters.
Therefore, the answer is 576.