Try this GRE question that tests your understanding of finding areas of shaded regions, and also on how the areas of similar triangles are related to the ratios of lengths of the corresponding sides of the two triangles.

In the triangle $ABC$ shown above the line segments $BA$, $DE$, and $FG$ are parallel to each other. The lengths of segments $BD$, $DF$ and $FC$ are in the ratio of $1$ to $2$ to $3$. What is the ratio of the area of the shaded region to the area of the unshaded region in triangle $ABC$ ?

- $\quad \dfrac{16}{27} $
- $\quad \dfrac{3}{4} $
- $\quad \dfrac{4}{5} $
- $\quad \dfrac{5}{6} $
- $\quad \dfrac{8}{9} $

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