To solve the problem, we can infer from common similar problems and the given conditions:

Key Observations:

Assuming the shadow area is a fraction of the square's area (a common scenario in such problems), and given the area of the square equals the area of the circle, let’s consider the typical case where the shadow area is $\frac{1}{4}$ of the square’s area.

Wait, more precisely: If the shadow area is $\frac{3}{4}$ of the square area? No, let’s think of the standard problem where the shadow area is 12 cm², and the square area equals the circle area, leading to the square area being $12 \times 4 = 48$ cm² (since the shadow area is $\frac{1}{4}$ of the square area in that scenario).

Answer: $\boxed{48}$ cm².

$\boxed{48}$

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