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
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
Updated On: Jul 20, 2026
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The Correct Option is B
Solution and Explanation
The graph below depicts both expressions. 
The desired area is equal to 4 times the area of the red triangle.
The area of the red triangle is calculated using the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Given the values, we compute: \[ \text{Area} = \frac{1}{2} \times 1 \times 1 = \frac{1}{2} \text{ square units} \]
Therefore, the required area is: \[ 4 \times \frac{1}{2} = 2 \text{ square units} \]
Final Answer: \( \boxed{2} \) square units
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