Attempt: I think the lower bound is 0 (exclusive) as can have the degenerate case of side lengths 1,1,2. As for the upper bound, I'm not sure but, perhaps $\sqrt3$ (inclusive)? This comes from the equilateral triangle of side lengths 2,2,2 and this is the biggest by symmetry (?).
Also, if there's any general result on this when the side lengths are in any ranges (not necessarily equal ranges) then please let me know.
Yes, you're right. The bounds are $\sqrt {3} \geq A > 0$, where $A$ is the area of the triangles formed.In general, given the range of side lengths, then the lower bound is trivially zero(exclusive) and upper bound is the area of the equilateral triangle formed from side length equal to the greatest length of the sides permissible. This follows from the fact that, given any three numbers whose sum is fixed, their product is maximum when they are equal. The sum is to be fixed by using the triangle inequality, which gives maximum sum only when the three sides are each equal to the greatest length permissible.