The attenuation of low-frequency sound has been a challenging task because the intrinsic dissipation of materials is inherently weak in this regime. Here we present a thin-film acoustic metamaterial, comprising an elastic membrane decorated with asymmetric rigid platelets that aims to totally absorb low-frequency airborne sound at selective resonance frequencies ranging from 100-1,000 Hz. Our samples can reach almost unity absorption at frequencies where the relevant sound wavelength in air is three orders of magnitude larger than the membrane thickness. At resonances, the flapping motion of the rigid platelets leads naturally to large elastic curvature energy density at their perimeter regions. As the flapping motions couple only minimally to the radiation modes, the overall energy density in the membrane can be two-to-three orders of magnitude larger than the incident wave energy density at low frequencies, forming in essence an open cavity.