Three-dimensional semimetals have been predicted and demonstrated to have a wide variety of interesting properties associated with its linear energy dispersion. In analogy to 2D Dirac-materials, such as graphene, Cd3As2 has also shown to exhibit ultra-high mobility, with values exceeding 15,000 cm2/V.s at room-temperature and much higher mobility at low temperatures. Furthermore, based on ARPES data Cd3As2 has been shown to exhibit a very large Fermi velocity, vF ~1.5x106 m/s, which is much higher than that in graphene (~1x106 m/s) or topological insulators. We experimentally demonstrate synthesis of high-quality large-area Cd3As2 thin-films through thermal evaporation and molecular beam epitaxy as well as the realization of plasmonic structures consisting of periodic arrays of Cd3As2 disks and stripes. These arrays exhibit sharp plasmonic resonances at terahertz frequencies (~1 THz) with associated quality-factors ~5. These quality-factors, which to the best of our knowledge are among the largest reported to-date at room-temperature in semiconductor-based plasmonic structures in the terahertz range, is a direct result of the long relaxation-time in Cd3As2, which in our films approaches 1 ps at room-temperature. Moreover, ultrafast tunable response is demonstrated through excitation of photo-induced carriers in optical pump / terahertz probe experiments. Our results evidence that the 3D nature of Cd3As2 provides for a more robust platform for terahertz plasmonic applications than what is otherwise possible in 2D Dirac-materials such as graphene. Overall, these observations can pave a way for the development of a myriad of terahertz optoelectronic devices based on Cd3As2, benefiting from strong coupling of terahertz radiation, ultrafast transient response, magneto-plasmon properties, etc.; moreover, the long Drude 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.