Consider a square with vertices at \( (1,1),(-1,1),(-1,-1) \) and \( (1,-1) \). If \( S \) is th...

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Consider a square with vertices at \( (1,1),(-1,1),(-1,-1) \) and \( (1,-1) \). If \( S \) is the region consisting of all points inside the square which are nearer to the origin than to any edge. Then, sketch the region \( S \) and find its area.
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