7. Given that $A B C$ is a triangle with $D$ being the midpoint of $A C$ and $E$ a point on $C B$ such that $C E=2 E B$. If $A E$ and $B D$ intersect at point $F$ and the area of $\triangle A F B=1$ unit, find the area of $\triangle A B C$.
(A) 3
(B) $\frac{10}{3}$
(C) $\frac{11}{3}$
(D) 4
(E) 5
7. Answer: (D)
Construct a line joining $C$ and $F$. Then using $[X Y Z]$ to denote the area of $\triangle X Y Z$, we know that $[A D F]=[D C F]=x$ and if $[B F E]=z$, then $[F C E]=2 z$.
Furthermore, we have $[A D B]=[D C B]$ i.e. $x+1=x+3 z$, so $z=\frac{1}{3}$.
Also, $2 \times[A E B]=[A C E]$ i.e. $2+2 z=2 x+2 z$, so $x=1$.
In conclusion, $[A B C]=1+2 x+3 z=4$ units.