Recently, the area coverage problem has emerged in the directional sensor network (DSN), where the sensor's sensed area depends on its working direction and viewing angle. This study has proposed a new algorithm based on the Voronoi diagram, called prioritized geometric area coverage (PGAC), to increase DSN's covered area. In a Voronoi diagram, all internal points of a convex polygon (cell) formed around a sensor are closer to the sensor than any other sensor. Therefore, the best sensor for covering a Voronoi cell area is the corresponding sensor of the cell. In contrast to similar approaches, PGAC considers the relation between the cell area and the sensor's covered area when selecting a sensor's working direction. It categorizes Voronoi cells, based on their geometric sizes, into three categories. In each category, PGAC adjusts the sensor's working direction to maximize the covered area and minimize the overlapping between adjacent cells. It also turns off redundant sensors for extending the network lifetime. Our simulation results showed that PGAC increases the covered area and decreases the number of active sensors compared to similar methods. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.