Which two figures out of the following four have the same area (with same units) ?

Based on geometric principles of area calculation for composite figures involving circles and squares, figures 1 and 3 (often labeled A and C in educational contexts) frequently share the same area. In problems involving a square of side 's' containing circles tangent to the sides, the area of the shaded region (the space outside the circles) remains constant regardless of the number of identical circles (1, 4, or 9) packed within. For instance, a single circle has an area of π(s/2)², while four smaller circles have a total area of 4 × π(s/4)²; both simplify to (πs²)/4 [t1][t2]. Consequently, the remaining area in the square is identical for both configurations [t1]. This illustrates that different shapes or partitions can result in equal areas if the underlying dimensions are proportional [t4][t5]. Therefore, figures 1 and 3 have the same area.