Can one deduce whether a given quantity is possible as the area of a triangle when supplied with the length of two of its sides? Recently I have found a question like following:


  In triangle $ABC$, $AB=AC=2$. Which of the following could be the area of
  triangle $ABC$? Indicate all possible areas:
  
  [A] $0.5$ [B] $1.0$ [C] $1.5$ [D] $2.0$ [E] $2.5$ [F] $3.0$


From my points of view, I can only guess one answer if I assume the triangle is a right angle triangle. In that case, the area will be $2$.


  But the answer showed the result, [A][B][C][D].


So, my question this is there any axiom that the area of the right angle will be the highest area of any type of triangle with the expressing two lengths of it?

Thanks in advance.
Not an axiom, but yes:  The area of a triangle is $\frac{1}{2}ab \sin \theta$, where $a$ and $b$ are two known side lengths and $\theta$ is the angle between the two given side lengths.  Since $\sin \theta$ reaches its maximum value when $\theta=90°$ (in which case we have $\sin 90° = 1$), the largest possible area is indeed attained for the case of a right angle.
No it is not possible to deduce just by two sides, because we don't know the angle between those two sides, which will decide how much area triangle will cover.
Take two lines of  $5$cm each and keep on changing the angle $(b,w)$ from $0$ to $180°$, you'll find that just two sides isn't enough.