Proof of Menelaus using areas

Question

I've tried to proof Menelaus' theorem using areas, but I've didn't figure out how. Some suggestions would be appreciated.

Menelaus' Theorem states :

Given a triangle ABC and a transversal line that crosses BC, AC and AB at points D, E and F respectively, with D, E and F distinct from A, B and C, then :

$$\frac{AF}{FB} * \frac{BD}{DC} * \frac{CE}{EA} = 1 $$

So far, I've proved Van Aubel's and Ceva's Theorem using areas, but I got stuck at Menelaus.

First, I taught $\frac{[ACB]}{[BCF]} = \frac {AB}{BF}$. And I've applied this for few more triangles, but it didn't work.

(I've noted with $[ABC]$ the area of triangle ABC).

Thanks!