In most of industrial applications of rotating machines, the acoustic scattering by surrounding surfaces should be taken into account, as for cooling fans placed on the back of a cooling unit or aircraft Environmental Control Systems (ECS) fan located in a duct. The present paper proposes to combine an extension of Amiet's theory for trailing-edge noise with a BEM solver. The method is validated on an airfoil test case, investigated experimentally at the Université de Sherbrooke, in which a scattering plate is used as complementary scattering surface. The necessary inputs for Amiet's theory are obtained using a RANS computation of the test setup, from which the trailing-edge wall-pressure spectrum is reconstructed using a stochastic model. The comparison of the experimental results with the numerical method proves the necessity to take surrounding surfaces such as support plates into account as scattering objects. Then, the effect of the extra scattering plate is correctly reproduced compared to the free-field prediction, except in the low frequency range, where other sound mechanisms are probably neglected in the present approach.