To effectively detect the targets in any direction, the radar antenna should be in the form of a planar array that has a large number of elements. In such a case, partially adaptive planar arrays, where only a few elements are adaptive, are often necessary to reduce the system's cost and increase the speed of the tracking capability. In this paper, only the perimeter elements of the planar arrays are selected to be adaptive while maintaining the good radiation characteristics as that of the fully adaptive planar arrays with, of course, lower cost and fewer RF components. Unlike a previous method that consists of optimizing only two edge elements in the linear arrays, the proposed planar array with optimized perimeter elements is quite sufficient to provide enough degrees of freedom to control the sidelobe pattern and place the desired nulls efficiently. Simulation results show that the required radiation pattern with asymmetric sidelobes and desired nulls can be obtained by optimizing only the perimeter elements of the planar arrays, while the interior elements are left unchanged.