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?
 A: Let (area of) $\triangle ECF = x$.
Then $\triangle FCD = \triangle ECF = x$ (same base, same height - I'll just call this SBSH for brevity).
So $\triangle ECD = 2x$ and $\triangle EBC = \triangle ECD = 2x$ (SBSH)
Hence $\triangle EBD = 4x$ and $\triangle AED = \triangle EBD = 4x$ (SBSH)
Therefore $\triangle ABD = 8x = 8\triangle CEF \ \ (QED)$
A: Well $\triangle$AED=$\frac{1}{2}\triangle ABD$.
So the problem reduces to showing that
$$\triangle CEF = \frac{1}{4} \triangle BED$$
Since F is the midpoint of ED, we have by similarity that:
$$|EB| = 2|FB|$$
in other words: 
$$\triangle CFD = \frac{1}{4} \triangle BED$$
Likewise, also by similarity,
$$\triangle BEC = \frac{1}{4} \triangle ABD = \frac{1}{2} \triangle BED$$
Which implies immediately that $\triangle CEF = \frac{1}{4} \triangle BED$, and hence we are done.
Note that the factors of 1/4 come from the scaling of both the base and the height by 1/2 due to similarity, hence the area is scaled by $(1/2)^2 = 1/4$ due to similarity.
The scaling factor of 1/2 for the bases and heights follows from the fact that the relevant line segments are medians and the midpoint theorem and the subsequent similarity.
A: 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.)
A: Hint: Here are the eight triangles:

(Large Version)
A: ED is the median of △(ABD) and therefore △(AED)=△(BED)=1/2 x △(ABD). 
EC is the median of △(BED) and therefore △(EBC)=△(ECD)=1/2 x △(BED). 
CF is the median of △(ECD) and therefore △(CEF)=△(CDF)=1/2 x △(ECD). 
From the three equations above △(CEF)=1/8 x △(ABD)
or 8 x △(CEF)=△(ABD)
