Circumference is a boundary length, so it uses linear units. Area is surface, so it uses square units. Because d=2r, C=πd and C=2πr are the same relationship.
Area grows with r². A rough check is useful: because π≈3.14, the area lies between 3r² and a little more; the AC9 elaboration also motivates that a circle’s area sits between 2r² and 4r². Rearranging many thin sectors alternately produces a near-rectangle with height r and base about πr, explaining A≈πr².
Preserve practical and cultural contexts: edging circular tables, deducing one circle measure from another, and exploring the significance/use of circles in traditional weaving designs with appropriate local cultural guidance rather than treating them as decoration.