Abstract: The definition of radiative direct-exchange areas(DEA) are usually involves four~sixfold integral in solution, and long-time computation is therefore unavoidable if using direct integral, thus restricting greatly the application of zone model. Then, the expressions of a reduced integration scheme are derived from conventional integral formulae to solve the radiative direct-exchange areas, and the Gaussian quadrature is introduced into the solutions to the radiative direct-exchange areas within 3-D closed system by either the reduced integration scheme or the direct integral. Compared with the result by direct integral, the result by reduced integration scheme not only satisfies well both the reciprocity and integrality as required by the radiative direct-exchange areas but also improves the computing accuracy with computing time shortened greatly.