Question:
Let S be the set of all points (x, y) in the x-y plane such that | x | + | y | ≤ 2 and | x | ≥ 1. Then, the area, in square units, of the region represented by S equals
Correct Answer: 2
The below figure shows the graph of both the expressions.
The required area = $4 \times$ the area of red triangle.
Area of red triangle =$\frac{1}{2}\times 1\times 1=\frac{1}{2}$ sq. units
Therefore, the required area = $4\times \frac{1}{2}=2$
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