【Analysis and Solution】
Geometry, equal area transformation.
Since $E D=3 A D$; therefore $S_{\triangle B D E}=3 S_{\triangle A B D}$;
Since $S_{\triangle B D E}=18$ square centimeters; therefore $S_{\triangle A B D}=18 \div 3=6$ square centimeters; therefore $S_{\triangle A B E}=6+18=24$ square centimeters;
Since $B E=3 E C$; therefore $S_{\triangle A B E}=3 S_{\triangle A C E}$; therefore $S_{\triangle A C E}=24 \div 3=8$ square centimeters; therefore $S_{\triangle A B C}=8+24=32$ square centimeters.
【Question 2】As shown in the figure, given $B E=3 E C, E D=3 A D$, the area of triangle $B D E$ is 18 square centimeters, then the area of triangle $A B C$ is. $\qquad$square centimeters.