Problem based on area of triangle In the figure, E,C and F are the mid points of AB, BD and ED respectively. Prove that: $8\triangle CEF=\triangle ABD$

From the given,
$ED$ is the median of $\triangle ABD$
So, $\triangle AED=\triangle BED$
Also, by mid point Theorem 
$EC||AD$ and $CF||AB$.
Now, what should I do next?

Area BED = 1/2 Area ABD as BE = 1/2 BA and BD = BD. (so they have the same base but one has only half the height.
Area CED = 1/2 Area BED as CD = 1/2 BD and E = E. (One has half the base but they both have the same height.)
Area CFD = 1/2 CED as CD = CD and DF = 1/2 DE. (So they both have same base but one has half the height.)
