Recurrent neural networks (RNNs) trained on neuroscience-based tasks have been widely used as models for cortical areas performing analogous tasks. However, very few tasks involve a single cortical area, and instead require the coordination of multiple brain areas. Despite the importance of multi-area computation, there is a limited understanding of the principles underlying such computation. We propose to use multi-area RNNs with neuroscience-inspired architecture constraints to derive key features of multi-area computation. In particular, we show that incorporating multiple areas and Dale's Law is critical for biasing the networks to learn biologically plausible solutions. Additionally, we leverage the full observability of the RNNs to show that output-relevant information is preferentially propagated between areas. These results suggest that cortex uses modular computation to generate minimal sufficient representations of task information. More broadly, our results suggest that constrained multi-area RNNs can produce experimentally testable hypotheses for computations that occur within and across multiple brain areas, enabling new insights into distributed computation in neural systems.