With given sides occurs when the quad is inscribable in (i.e. inscribed in) a circle (and this indeed does not depend on the order of the sides due to Brahmagupta's area formula). It is also interesting that the "max area happens when quad inscribable" theorem is an "absolute" theorem, i.e. it works in both euclidean and nonEuclidean geometries. And the fact the area then is independent of the side-ordering also is "absolute" (which should be obvious). (I'm recounting all this from memory, since I recall proving this theorem a long time ago. I was going to put it in a paper I never finished.)