Step-by-step Solution:

To plot the graph of \( |x| + |y| = 2 \), we rewrite it as: \[ |x| + |y| = 2 \implies x, y \text{ satisfy: } \begin{cases} x + y = 2, \\ x - y = 2, \\ -x + y = 2, \\ -x - y = 2. \end{cases} \] These equations correspond to lines intersecting the axes at \( (2, 0), (-2, 0), (0, 2), (0, -2) \), forming a square with these vertices. The area of the square can be computed as: \[ \text{Area of the square} = 4 \times \text{Area of one triangle}. \] The area of one triangle (formed by the origin and two adjacent vertices) is: \[ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 2 = 2. \] Thus, the area of the square is: \[ 4 \times 2 = 8. \]