  The scaling behavior of the entanglement entropy in the two-dimensional
random transverse field Ising model is studied numerically through the strong
disordered renormalization group method. We find that the leading term of the
entanglement entropy always scales linearly with the block size. However,
besides this \emph{area law} contribution, we find a subleading logarithmic
correction at the quantum critical point. This correction is discussed from the
point of view of an underlying percolation transition, both at finite and at
zero temperature.
