Sensor coverage varies with location due to factors such as weather, terrain, and obstacles. If a field can be partitioned into zones of homogeneous sensing areas, then coverage by a random deployment of sensors can be optimized by controlling the number of sensors deployed in each zone. We derive expressions to directly calculate the optimal sensor partition in runtime asymptotically equal to the number of zones. We further derive expressions to determine the minimum sensor count required to achieve a specific coverage threshold. We bound the maximum increase in coverage over a strategy oblivious to differences in sensing areas, which our results show is no greater than 13% for a field with two zones. While the analytical solutions assume that each zone is covered independently, we allow sensors to affect neighboring zones in simulations. Nevertheless, the simulations support the optimality of our solution.