Question 82
Let $A B C D E F$ be a convex hexagon with the following properties.
a. $\overline{A C}$ and $\overline{A E}$ trisect $\angle B A F$.
b. $\overline{B E} \parallel \overline{C D}$ and $\overline{C F} \parallel \overline{D E}$.
c. $A B = 2 A C = 4 A E = 8 A F$.
Suppose that quadrilaterals $A C D E$ and $A D E F$ have area $2014$ and $1400$, respectively. Find the area of quadrilateral $A B C D$.
Supplemental exact coordinate figure.
a. $\overline{A C}$ and $\overline{A E}$ trisect $\angle B A F$.
b. $\overline{B E} \parallel \overline{C D}$ and $\overline{C F} \parallel \overline{D E}$.
c. $A B = 2 A C = 4 A E = 8 A F$.
Suppose that quadrilaterals $A C D E$ and $A D E F$ have area $2014$ and $1400$, respectively. Find the area of quadrilateral $A B C D$.
Supplemental exact coordinate figure.