Wireless sensor networks are made up of hundreds of devices deployed over a distant or sensitive field to be monitored. Energy consumption is balanced by taking advantage of the redundancy induced by the random deployment of nodes. Some nodes are active while others are in sleep mode, thus using less energy. Such a dynamic topology should not impact the monitoring activity. Area coverage protocols aim at turning off redundant sensor nodes while ensuring full coverage of the area by the remaining active nodes. Providing k-area coverage therefore means that every physical point of the monitored field is sensed by at least k sensor devices. Connectivity of the active nodes subset must also be provided so that monitoring reports can reach the sink stations. Existing solutions hardly address these two issues as a unified one. In this paper, we propose a localized algorithm for multiple sensor area coverage able to build connected active nodes sets. We also show that a simple feature of the protocol, called the coverage evaluation scheme, can be enhanced to handle various k-area coverage problem definitions. Experimental results show that our coverage scheme is resistant to collisions of messages as k-area-coverage of the deployment area and connectivity of the active nodes set can still be ensured.