Using the physical optics method, asymptotic expressions have been obtained for the cross sections and efficiency factors of extinction and scattering when one of the linear dimensions of a rectangular plate tends to infinity. It has been found that for this scattering problem the error of the physical optics method depends on the values of two definite integrals. Each of them is an asymptotic expression of corresponding double integral obtained for rectangular plate. It is shown that estimate of the systematic error is essentially simplified with the use of asymptotic expressions instead of double integrals.