We report observations of potentially hazardous, Apollo-class asteroid 1981 Midas, which passed 0.090 au from Earth (35 lunar distances) on March 21, 2018. During this close approach, Midas was observed by radar both from the Arecibo Observatory on March 21 through 25 (five nights), and from NASA's Goldstone Deep Space Communications Complex on March 19 and 21. These radar observations yielded one-dimensional continuous-wave spectra and two-dimensional delay-Doppler images. In addition, there have been optical lightcurve observations of Midas during four apparitions (1987, 1992, 2004, and 2018), which showed a rotation period of 5.22 hours. Midas has an absolute magnitude of H = 15.2. By combining the lightcurves and radar data, we have constructed a shape model for Midas. This model shows that Midas has two lobes separated by a neck which, at its thinnest point, is about 60% of the width of the lobes. From our model, we also confirm the lightcurve-derived rotation period and show that Midas has dimensions of 3.33 x 1.99 x 1.85 km +/- 10% and a pole position within 6 degrees of (370,-610) in ecliptic longitude and latitude.

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