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For a square with side length \( s = 10 \) cm the diagonal \( d \) is given by:
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\[
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d = s\sqrt{2} = 10\sqrt{2} \ \text{cm}
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\]
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This diagonal is the diameter of the circle. The radius \( r \) of the circle is half of the diameter:
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\[
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r = \frac{d}{2} = \frac{10\sqrt{2}}{2} = 5\sqrt{2} \ \text{cm}
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The area \( A \) of the circle is:
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\[
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A = \pi r^2 = \pi (5\sqrt{2})^2 = \pi \times 25 \times 2 = 50\pi \ \text{cm}^2
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\]
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