This paper is concerned with the study of local decay rates of the energy associated to a semilinear wave equation in an inhomogeneous medium with frictional localized damping. The problem is considered in Omega subset of R-n, an open, bounded, and connected set, n >= 2, with smooth boundary Gamma = Gamma(0) boolean OR Gamma(1) such that (Gamma) over bar (0) boolean AND (Gamma) over bar (1) = empty set. On Gamma(0) we consider the homogeneous Dirichlet conditions while on Gamma(1) we consider the acoustic boundary conditions with source term and nonlinear frictional dissipation. To prove the main result we used the microlocal analysis tools of Burq and Gerard [Controle Optimal des equations aux derivees partielles, 2001] combined with Lasiecka and Tataru [Differential Integral Equations, 6 (1993), pp. 507-533] arguments and a construction of an appropriate damping region which can be considered with measure as small as desired, however totally distributed on Omega.