Area measurement is a foundational component across STEM fields. The area formula offers limited insight for children trying to develop their area measurement reasoning skills, particularly when dealing with composite shapes. Spatial structuring, where children explore structural units of a 2D space, is an alternative approach. However, poor manipulation of physical units can reinforce misconceptions about area measurement. To address this issue, we developed MeoGeo, an augmented reality (AR) smartphone application. MeoGeo allows children to readily create virtual structural arrays with units of varying sizes, superimposing them on their surroundings in real-time. We conducted an exploratory multiple-case study over a 7-week program to examine the effect of AR activities. Data included written responses from three elementary students on paper-and-pencil tests, along with in situ videos recordings. Our findings indicate that engagement in AR activities facilitated reasoning skills in area measurement for both basic and composite shapes. Furthermore, students maintained their reasoning skills beyond the intervention period. Our study underscores the importance of developing AR systems that align explicitly with the developmental progression of each child, and it highlights the critical role of the instructor in effective execution of AR activities.