Recent work has considered personalized route planning based on user profiles, but none of it accounts for human trust. We argue that human trust is an important factor to consider when planning routes for automated vehicles. This paper presents a trust-based route planning approach for automated vehicles. We formalize the human-vehicle interaction as a partially observable Markov decision process (POMDP) and model trust as a partially observable state variable of the POMDP, representing the human's hidden mental state. We build data-driven models of human trust dynamics and takeover decisions, which are incorporated in the POMDP framework, using data collected from an online user study with 100 participants on the Amazon Mechanical Turk platform. We compute optimal routes for automated vehicles by solving optimal policies in the POMDP planning, and evaluate the resulting routes via human subject experiments with 22 participants on a driving simulator. The experimental results show that participants taking the trust-based route generally reported more positive responses in the after-driving survey than those taking the baseline (trust-free) route. In addition, we analyze the trade-offs between multiple planning objectives (e.g., trust, distance, energy consumption) via multi-objective optimization of the POMDP. We also identify a set of open issues and implications for real-world deployment of the proposed approach in automated vehicles.