Example 1. As shown in the figure, in quadrilateral $ABCD$, points $E$, $F$ are on $BC$, $CD$ respectively, and $\frac{DF}{FC}=1$, $\frac{E}{B}=2$. If the area of $\triangle ADF$ is $m$, and the area of quadrilateral $AECF$ is $n(n>m)$, find the area of quadrilateral $ABCD$. (1989, National Junior High School League)
Connect $A C$.
Since $\triangle A D F$ and $\triangle A F C$ have the same height and base, we have $S \triangle \triangle \triangle^{\mathrm{B}}=S \triangle \triangle D F=m$.
Then $S_{\triangle \triangle P}=S_{\triangle E C E}-S \triangle \triangle F C=n-m$. Also, $\triangle A B E$ and $\triangle A C_{E}$ have the same base,

and $C E: E B=2$, so $\frac{S \triangle \triangle C B}{S \triangle \triangle B B}=\frac{C E}{E B}=2$,

which gives $S_{\triangle B E}=\frac{1}{2} S_{\triangle A C B}$
$$
\begin{array}{l}
=\frac{1}{2}(n-m) . \\
\text { Therefore } S_{\mathrm{AB}(1)} \\
=\frac{1}{2}(3 n+m) .
\end{array}
$$