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Three-dimensional (3D) semimetals have been predicted and demonstrated to have a wide variety of interesting properties associated with its linear energy dispersion. In analogy to two-dimensional (2D) Dirac semimetals, such as graphene, Cd3As2, a 3D semimetal, has shown ultra-high mobility, large Fermi velocity, and has been hypothesized to support plasmons at terahertz frequencies. In this work, we demonstrate synthesis of high-quality large-area Cd3As2 thin-films through thermal evaporation as well as the experimental realization of plasmonic structures consisting of periodic arrays of Cd3As2 stripes. These arrays exhibit sharp resonances at terahertz frequencies with associated quality-factors (Q) as high as ~ 3.7. Such spectrally-narrow resonances can be understood on the basis of a large kinetic-inductance, resulting from a long momentum scattering time, which in our films can approach ~1 ps at room-temperature. Moreover, we demonstrate an ultrafast tunable response through excitation of photo-induced carriers in optical pump / terahertz probe experiments. Our results evidence that the intrinsic 3D nature of Cd3As2 provides for a very robust platform for terahertz plasmonic applications. Overall, our observations pave a way for the development of myriad terahertz (opto) electronic devices based on Cd3As2 and other 3D Dirac semimetals, benefiting from strong coupling of terahertz radiation, ultrafast transient response, magneto-plasmon properties, etc. Moreover, the long momentum scattering time, thus large kinetic inductance in Cd3As2, also holds enormous potential for the re-design of passive elements such as inductors and hence can have a profound impact in the field of RF integrated circuits., Comment: 32 pages, 8 figures