During wind farm planning, the farm layout or turbine arrangement is generally optimized to minimize the wake losses, and thereby maximize the energy production. However, the scope of layout design itself depends on the specified farm land-shape, where the latter is conventionally not considered a part of the wind farm decision-making process. Instead, a presumed land-shape is generally used during the layout design process, likely leading to sub-optimal wind farm planning. In this paper, we develop a novel framework to explore how the farm land-shape influences the output potential of a site, under a given wind resource variation. Farm land-shapes are defined in terms of their aspect ratio and directional orientation, assuming a rectangular configuration. Simultaneous optimizations of the turbine selection and placement are performed to maximize the energy production capacity, for a set of sample land-shapes with fixed land area. The maximum farm capacity factor or farm output potential is then represented as a function of the land aspect ratio and land orientation, using quadratic and Kriging response surfaces. This framework is applied to design a 25 MW wind farm at a North Dakota site that experiences multiple dominant wind directions. An appreciable 5% difference in capacity factor is observed between the best and the worst sample farm land-shapes at this wind site. It is observed that among the 50 sample land-shapes, higher energy production is accomplished by the farm lands that have aspect ratios significantly greater than one, and are oriented lengthwise roughly along the dominant wind direction axis. Subsequent optimization of the land-shape using the Kriging response surface further corroborates this observation.