Masses of the short-lived radionuclides 32Ar (T(1/2)=98 ms) and 33Ar (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 32Ar will allow for a better constraint on scalar contributions to the weak interaction. New mass values have also been measured for 44Ar and 45Ar, and a 20sigma deviation for 44Ar from the literature value was found and interpreted.