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The shape demagnetizing factors of a planar magnetic insulator are of some interest in the design of a number of microwave ferrite components. One means of experimentally evaluating these quantities, in the case of a disk geometry, is to measure the Kittel line and to make use of a standard identity. Another method, introduced here, is to extract the axial demagnetizing factor by having recourse to the intersections of the split branches of a gyromagnetic resonator. The letter includes measurements on the axial demagnetizing factor of an irregular hexagonal geometry for three different values of saturation magnetization.