As shown in the figure, triangle $A B C$ is folded along segment $D E$, resulting in a heptagon $A D E C F G H$. If the area ratio of the heptagon to the original triangle is
$5: 7$, and the area of the overlapping part after folding is $8 \mathrm{~cm}^{2}$, find the area of the original triangle $A B C$.
Geometry, Area; Ratio Correspondence.
Because $S_{\text {heptagon ADECFGH }}: S_{\triangle A B C}=5: 7$;
and because the area by which $\triangle A B C$ is larger than heptagon $A D E C F G H$ is exactly the shaded part;
thus $S_{\text {heptagon } A D E C F G H}: S_{\triangle A B C}: S_{\text {shaded }}=5: 7: 2$;

Given that $S_{\text {shaded }}=8$ square centimeters;

Therefore, $S_{\triangle A B C}=8 \div 2 \times 7=28$ square centimeters.