We provide closed-form approximations to the performance gain achieved in a RIS-assisted communication. We then consider a network deployment of RIS and Transmitter-Receiver pairs and use these approximate expressions to provide equivalence models which state that the performance of a RIS-equipped network is similar to the performance of an appropriately spatially scaled system. We provide a way of assigning available RIS to assist communication between several transmitter-receiver pairs. Several such approximations are expected to spawn from this study, with more clarity on structural aspects of the gains achieved in RIS-assisted communications.