Heron's formula for the area A of a triangle with
sides a,b, and c is

 where 

We will eventually let , , ,
and 

But to make things easier we will first simplify
Heron's formula by first removing the square root and
secondly, eliminating s:





where





so, substituting to eliminate s,









Now that we have rewritten Heron's formula in terms of the
sides only, we simplify the factors to substitute in
the above revised version of Heron's formula, which I think
is superior to the original version, especially for 
calculating purposes.

So now we substitute , , , and 







Substituting these factors:







Divide both sides by 3















The only real positive solution is
gotten by setting the first factor = 0




Edwin