In this pedagogical action research study, we, as post-secondary mathematics teacher educators, built on an existing effort to improve pre-service teachers' mathematical vocabulary understandings by intentionally addressing their struggles related to polygonal area formulas. Utilizing cognitive load theory and Bruner's levels of developmental learning, we adapted and refined an existing "Area of Polygons" lesson to eliminate extraneous elements and scaffold the introduction of essential elements in the context of a cognitively engaging activity. Comparing our resulting lesson components to existing literature on polygonal area, we found two main approaches towards exploring area of polygons. Both approaches emphasized conservation of polygonal area with one focused on the details of attributes and square units and the other focused on comparisons of areas of figures. We discuss the implications of these approaches and the use of cognitive load theory in tandem with Bruner's levels for future curriculum redesign.