10. As shown in the right figure, in triangle $\mathrm{ABC}$, $\mathrm{AD}=2 \mathrm{BD}$, $\mathrm{AD}=\mathrm{EC}$, $\mathrm{BC}=18$, the area of triangle $\mathrm{AFC}$ is equal to the area of quadrilateral DBEF. What is the length of AB?
Parse: Let the area of triangle $A B C$ be “1”, $A D=2 B D$, so $\triangle \triangle D C B=\frac{1}{3}$, the area of triangle AFC is equal to the area of quadrilateral DBEF, adding triangle EFC to both, the areas should still be equal, so $\triangle \triangle A E C=\frac{1}{3}$, thus, $E C=\frac{1}{3} B C=\frac{1}{3} \times 18=6, A D=E C, A D=\frac{2}{3} A B$, so $A B=6 \div \frac{2}{3}=9$