Resonantly absorbing thin films comprising periodically sub-wavelength structured metal surface, dielectric spacer, and metal ground plane are a topic of current interest with important applications. These structures are frequently described as "metamaterials", where effective permittivity and permeability with dispersion near electric and magnetic resonances allow impedance matching to free space for maximum absorption. In this paper, we compare synchrotron-based infrared spectral microscopy of a single isolated unit cell and a periodic array, and we show that the resonances have little to do with periodicity. Instead, the observed absorption spectra of usual periodically structured thin films are best described as due to standing-wave resonances within each independent unit cell, rather than as due to effective optical constants of a metamaterial. The effect of having arrays of unit cells is mainly to strengthen the absorption by increasing the fill factor, and such arrays need not be periodic. Initial work toward applying the subject absorbers to room-temperature bolometer arrays is presented.