In this paper, we study the trajectory and resource optimization for lightweight rotary-wing unmanned aerial vehicles (UAVs) equipped with a synthetic aperture radar (SAR) system. The UAV's mission is to perform SAR imaging of a given area of interest (AoI). In this setup, real-time communication with a base station (BS) is required to facilitate live mission planning for the drone. For this purpose, a non-convex mixed-integer non-linear program (MINLP) is formulated such that the UAV resources and three-dimensional (3D) trajectory are jointly optimized for maximization of the drone radar ground coverage. We present a low-complexity sub-optimal algorithm based on successive convex approximation (SCA) for solving the problem, and perform a finite search to optimize the total distance traversed by the UAV for maximal coverage. We show that the proposed 3D trajectory planning achieves at least 70% improvement in radar ground coverage compared to benchmark schemes employing constant powers for communication or radar imaging. We also show that positioning the BS near the AoI can significantly improve the radar coverage of the UAV.