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Cooperative communication for wireless networks has been extensively investigated from the perspective of physical-layer design. However, the impact of physical-layer cooperation on the network-layer routing design still remains unclear. In this paper, we examine the potential benefit of radio coverage extension from cooperation, and present how to incorporate this feature into the routing design. Specifically, with a series of mathematical formulations and derivations, we quantitatively identify direct and cooperative radio coverages based on the average symbol error rate (SER) performance requirement, elucidating how cooperative diversity gain can be translated into radio coverage extension. We then propose a cooperative geographic routing protocol with cross-layer design, namely the Relay-Aware Cooperative Routing (RACR) protocol, that exploits the merit of radio coverage extension for improving the non-cooperative geographic routing. Simulation results show that the RACR protocol performs significantly better than the non-cooperative geographic routing in terms of the average path length in dense ad hoc networks.