The area of the region satisfying the inequalities |x| - y ≤ 1, y ≥ 0 and y ≤ 1 is
Explanation:
Given,
|x| - y ≤ 1 ⇒ y ≥ |x| - 1
y ≥ 0 and y ≤ 1.
The following diagram can be drawn from the given information.
The required area is highlighted in orange i.e., a trapezium whose parallel sides are 4 units and 2 units and height is 1 unit.
∴ Area of the trapezium = 1/2 × (2 + 4) × 1 = 3 square units.
Hence, 3.
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