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The area \( A \) of the circle is:
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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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\boxed{50\pi \ \text{cm}^2}
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Question:** In a regular hexagon with a side length of 12 cm calculate the length of the longest diagonal.
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Solution:
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A regular hexagon can be divided into 6 equilateral triangles. The longest diagonal of the hexagon spans across two opposite vertices passing through the center and equals twice the side length.
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Given the side length \( s = 12 \) cm the longest diagonal \( D \) is:
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