7. In triangle $A B C$, the medians $A D$ and $B E$ meet at the centroid $G$. Determine the ratio of the area of quadrilateral $C D G E$ to the area of triangle $A B C$.
Answer: $\frac{1}{3}$
Solution:
Refer to the figure on the right.
$$
\begin{aligned}
{[C D G E] } & =[C D E]+[G E D] \\
& =\frac{1}{4}[A B C]+\frac{1}{3}[B E D] \\
& =\frac{1}{4}[A B C]+\frac{1}{3}\left(\frac{1}{4}[A B C]\right) \\
& =\frac{1}{4}[A B C]+\frac{1}{12}[A B C] \\
& =\frac{1}{3}[A B C]
\end{aligned}
$$