Masses of the short-lived radionuclides Ar-32 (T-1/2=98 ms) and Ar-33 (T-1/2=173 ms) have been determined with the Penning trap mass spectrometer ISOLTRAP. Relative uncertainties of 6.0x10(-8) (deltam=1.8 keV) and 1.4x10(-8) (deltam=0.44 keV), respectively, have been achieved. At present, these new mass data serve as the most stringent test of the quadratic form of the isobaric-multiplet mass equation. Furthermore, the improved accuracy for the mass of Ar-32 will allow for a better constraint on scalar contributions to the weak interaction. New mass values have also been measured for Ar-44 and Ar-45, and a 20sigma deviation for Ar-44 from the literature value was found and interpreted.