In remote sensing, a target generally has a random position and orientation with respect to the array of image pixels. We derive a simple analytic expression for the expectation value of the area of a rectangular target relative to the area of a square image pixel containing the target's centre point. The analytic result applies when the sides of the target and image pixel are parallel. We then consider the possibility of a random orientation of the target using a more general digital approach. Interestingly, we find that the analytic expression (ignoring orientational averaging) is quite adequate for practical applications.