>>The area does not solely depend on the angle ABC.
>if you put a constraint and let the segment AC constant,
>there's a straight relationship between �� and the
>altitude.

No, this is incorrect. AC is your base and has been fixed from the outset. For a given angle ABC point B may be anywhere on a circular arc, see

http://www.cut-the-knot.org/pythagoras/Munching/inscribed.shtml ,

with varying altitude.

>>Area(ABC) <= (b/2)2 �~ cot(��/2) / 2,
>can you give more insights on how you got this?

Draw a picture and try some trigonometry and do not forget the triangle ABC is supposed to be isosceles. Do try it.