Law of Cosines Proof This question is based on the diagram

taken from this link. I don't understand why the areas of A6 and A5 adds up to $2bc\cos(A)$.

If you look at A5. It is a rectangle with side $b$ and, say, $x$.
Now $\cos A= x/c$, so $x=c\cos A$. Hence the area of A5 is $bx=bc\cos A$. 
A similar argument tells you that the area of A6 is $cb\cos A$.
