【Question 9】
As shown in the figure, the side length of square $ABCD$ is 8 cm. Point $E$ is on the extension of $AB$, and quadrilateral $BEFG$ is a square. Find the area of triangle $AFC$.
【Analysis and Solution】
Geometry, Area, Equal Area Transformation.
Connect $B F$;
Since quadrilaterals $A B C D$ and $B E F G$ are both squares, i.e., $\angle B A C=\angle E B F=45^{\circ}$; thus $A C / / B F$;

Therefore, $S_{\triangle A F C}=S_{\triangle A B C}=8 \times 8 \div 2=32$ square centimeters.