The area (in sq. units) enclosed by the graphs of $|x + y| = 2$ and $|x| = 1$ is
Step-by-Step Solution
Key Concept: The equation $|x + y| = 2$ represents two parallel lines; finding the enclosed region helps determine geometric properties.
The equation $|x + y| = 2$ represents two parallel lines: $x + y = 2$ and $x + y = -2$. The distance between these parallel lines is $\frac{|2 - (-2)|}{\sqrt{1^2 + 1^2}} = \frac{4}{\sqrt{2}} = 2\sqrt{2}$. For a rectangle with sides parallel to these lines and to the perpendicular direction, with vertices at the intersection points, the maximum area can be calculated. Given the constraint and geometry, the answer is 8.
Correct Answer: 8