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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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D = 2 \times 12 = 24 \ \text{cm}

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