2012
Problem - 1935
In $\triangle{ABC}$, segments AB and AC have each been divided into four congruent segments. We must find the fraction of the triangle that is shaded.
Answer
$\frac{3}{8}$
Let the area of $\triangle{ADE}$ be $S$. Then the areas of $\triangle{AFG}$, $\triangle{AHI}$ and $\triangle{ABC}$ are $4S$, $9S$ and $16S$, respectively. It follows that the are of $DEGF$ is $3S$, or the shaded area is $6S$. Then the final answer is $$\frac{6S}{16S}=\boxed{\frac{3}{8}}$$