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The entanglement entropy of the random transverse-field Ising model iscalculated by a numerical implementation of the asymptotically exact strongdisorder renormalization group method in 2d, 3d and 4d hypercubic lattices fordifferent shapes of the subregion. We find that the area law is alwayssatisfied, but there are analytic corrections due to E-dimensional edges(1<=E<=d-2). More interesting is the contribution arising from corners, whichis logarithmically divergent at the critical point and its prefactor in a givendimension is universal, i.e. independent of the form of disorder.

Universal logarithmic terms in the entanglement entropy of 2d, 3d and 4d random transverse-field Ising models