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

• A. 1
• B. 2
• C. 4
• D. 3

Answer 1

The Correct Option is B

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