Consider a square with vertices at `(1,1),(-1,1),(-1,-1),a n d(1,-1)dot` Set `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.

Explanation

To solve the problem step by step, we will first analyze the square and then determine the region \( S \) that consists of points closer to the origin than to any edge of the square. Finally, we will calculate the area of this region.

### Step 1: Identify the Square
The vertices of the square are given as \( (1, 1), (-1, 1), (-1, -1), (1, -1) \). This square is centered at the origin and has a side length of 2.

### Step 2: Determine the Distance to the Edges
The edges of the square are located at:
- \( x = 1 \) (right edge)
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