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Consider a square with vertices at (1, 1...

Consider a square with vertices at `(1, 1), (-1, 1), (-1, -1) and (1, -1)`. Let S be the region consisting of all points inside the square which are nearer to the origin than to any edge. Sketch the region S and find its area.

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`(4)/(3) (4sqrt2 - 5)` sq. units
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