  We show that, apart from the usual area operator of non-perturbative quantum
gravity, there exists another, closely related, operator that measures areas of
surfaces. Both corresponding classical expressions yield the area. Quantum
mechanically, however, the spectra of the two operators are different,
coinciding only in the limit when the spins labelling the state are large. We
argue that both operators are legitimate quantum operators, and which one to
use depends on the context of a physical problem of interest. Thus, for
example, we argue that it is the operator proposed here that is relevant in the
black hole context to measure the area of black hole horizon. We show that the
difference between the two operators is due to non-commutativity that is known
to arise in the quantum theory. We give a heuristic picture explaining the
difference between the two area spectra in terms of quantum fluctuations of the
surface whose area is being measured.
