Consider the closed figure \( C \) made by the lines \( |x|+|y|-\sq...

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Consider the closed figure \( C \) made by the lines \( |x|+|y|-\sqrt{2} \). Let \( S \) be the region inside the figure \( C \) such that any point in it is nearer to the side \( x+y=\sqrt{2} \) than the origin. Then three times
\( \mathrm{P} \) the area of \( S \) is

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