Example 4. As shown in the figure, in $\triangle A B C$, $A D$ and $B E$ are both medians, $M N$ bisects $B E$ and is parallel to $A B$. It is also known that $A D$, $B E$, and $M N$ divide $\triangle A B C$ into six parts, with areas $a, b, c, d, e, 18$ respectively. Try to find the values of $a, b, c, d, e$. (Anqing City Second Junior High School Mathematics League)

Dividing the triangle into six parts with the medians $A D$ and $B E$, and the line $M N$ which bisects $B E$ and is parallel to $A B$, we need to determine the areas $a, b, c, d, e$.
Analyzing the six blocks where only one is known, using the center of gravity $G$ to divide the three medians into segments of $2:1$ and $H$ bisecting $B E$, and $M N / / A D$: we can obtain: $\frac{N H}{H M}=\frac{A G}{G}=2: 1 \Rightarrow a=9$,
$$
\begin{array}{l}
2 d=18+e, \\
d=a+b, \\
\dot{u}+c=a+b+e+18, \\
\frac{18+e}{18}=\left(\frac{\frac{2}{3} B E}{\frac{1}{2} B E}\right)^{2} .
\end{array}
$$

Solving the five equations simultaneously, we get: $a=9, b=7, c=32, d=16, e=$
14.