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This paper is aimed at developing an approximate and relatively simple but closed-form uniform geometrical theory of diffraction (UTD) solution for describing the radiated and scattered fields by an antenna near a complex platform consisting of a three-dimensional (3-D) thin material-coated metallic surface, including edges and corners. Unlike the previous works that consider primarily plane wave scattering, the developed solution can also treat radiation/scattering problems of antennas near finite material-coated metallic surfaces which are composed of edges and corners. The developed solution, which is formulated by using a heuristic approach, recovers the proper local plane wave Fresnel reflection coefficient. In addition, the developed UTD-diffracted fields will satisfy the radiation condition, boundary conditions on the conductor. The accuracy of the developed solution is verified by comparing with simulation results from a computer software. It is found that the results from our developed solution agree well with those of references. However, some small discrepancies occur but it is good enough for engineering applications. The proposed solution can be very useful for antenna engineers to design multiple antennas with an electrically large complex material-coated platform.