Prove that three medians divide a triangle into 6 triangles with equal surface area. I have attempted to solve this task:

I have drawn the medians and described the lengths of the segments.
I also noticed that triangles ADC and BCD share the same height, thus
$S_{total}= xh$ 
Whereas the surface of triangles ACD and BCD

$S= xh/2$ 
And so I have already made it so far as to get the halves. But I haven't got a faintest idea how to get to the sixths. 
I would be most grateful if you gave your answer in simple terms. Geometry is my Achilles's heel.

Apply an affine transformation to produce an equilateral triangle. Such a transformation preserves relative areas, and all the little triangles are now the same.
