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This article presents the Smart Quad, a tangible user interface (TUI) designed to enhance quadrilateral learning by integrating physical and digital educational tools. Developed through an iterative, user-centered design process, the Smart Quad is a tangible device that pairs with the PhET SimulationQuadrilateralcreating a multimodal, inclusive learning environment for geometry. We conducted a pilot study with four users with blindness or low vision (BLV) and a formal user study in two settings: a classroom study with 15 students from grades 6 to 8 and individual sessions with five students with BLV from grades 7 to 9. Our findings demonstrate the efficacy of the Smart Quad in facilitating hands-on, interactive learning experiences, particularly for students with BLV, and highlight the potential for TUIs to bridge gaps in mathematics education by supporting diverse learning needs and preferences. The results suggest that TUIs like the Smart Quad can significantly improve engagement and understanding of geometric concepts, offering a promising direction for future educational tools.