Mathematics - Geometry - Circles - Area of circles - Circle vs Square

Compare shapes: given the same PERIMETER (e.g., 40 units), which has more area: a square (side=10, area=100) or a circle (C=40, r=40/2π≈6.37, area≈127.3)? The circle wins! Given the same AREA (e.g., 100 sq units), which has less perimeter? The circle wins again! The student adjusts a shared value an