Square $abcd$ has area $200$. point $e$ lies on side $\overline{bc}$. points $f$ and $g$ are the midpoints of $\overline{ae}$ and $\overline{de}$, respectively. given that quadrilateral $begf$ has area $34$, what is the area of triangle $gcd$?

1. Consider square ABCD. You know that  

then

2. Consider traiangle AED. F is mipoint of AE and G is midpoint of DE, then FG is midline of triangle AED. This means that

3. Consider trapezoid BFGC. Its area is

where h is the height of trapezoid and is equal to half of AB. Thus,

4.

5. Note that angles EGC and CGD are supplementary and

Then

answer: the correct one is a

step-by-step explanation:

answer:

c. the third graph