Unmanned aerial vehicle (UAV) has attracted much attention due to its excellent ability to collect visual information of surroundings. In this paper, we investigate a new monitoring model to focus on sizes and shapes of objects, and occlusion between objects, and then study the placement of a set of UAVs to monitor polygonal sizable objects. Our aim is to maximize the overall monitoring utility of all objects by determining the positions and orientations of UAVs, given a set of polygonal sizable objects with fixed coordinates and shapes on a $2\mathbf{D}$ plane. We study two typical scenarios of the problem: the former stipulates that a line segment is effectively monitored only when it is completely monitored by a single UAV, and the latter allows multiple UAVs to cooperatively monitor a line segment and then integrate their image information. The problem is proved to be NP-hard with infinite continuous solution space. For the first scenario, we propose a $(1-1/e)$-approximation algorithm. For the second one, we first propose a 1/2-approximation algorithm to address its simple version, and then propose a heuristic solution. Numerical evaluations validate the effectiveness of our proposed algorithms.