【Question 20】
As shown in the figure, points $E$, $F$, $G$, and $H$ are the points on the four sides of square $ABCD$ that are closer to $B$, $C$, $D$, and $A$, respectively, dividing each side into three equal parts. If the side length of the square is 6, then the area of the shaded part is $\qquad$.
【Analysis and Solution】
Geometry, clever area calculation.
Connect $B H$;
Since points $E, F, G, H$ are the points on the sides of square $A B C D$ that are closer to $B, C, D, A$ and divide the sides into three equal parts;
Therefore, $A H=B E=D G=6 \times \frac{1}{3}=2, B F=D H=6 \times \frac{2}{3}=4$;
$$
\begin{array}{l}
S_{\triangle B E H}=B E \times A H \div 2=2 \times 2 \div 2=2 \\
S_{\triangle B F H}=B F \times A B \div 2=4 \times 6 \div 2=12
\end{array}
$$
$$
\begin{array}{l}
S_{\triangle D G H}=D G \times D H \div 2=2 \times 4 \div 2=4 ; \\
S_{\text {shaded }}=S_{\triangle B E H}+S_{\triangle B F H}+S_{\triangle D G H}=2+12+4=18 。
\end{array}
$$