\(|x| + |y| = 1\) is a square with vertices (1, 0), (0, 1), (−1, 0), (0, −1). Its diagonals lie along the axes and each has length 2.

Area of a square (rhombus) = \(\frac{1}{2} d_1 d_2 = \frac{1}{2} \times 2 \times 2 = 2\)

(Or: it has 4 congruent triangles, each with area \(\frac{1}{2} \times 1 \times 1\), so the total is 2.)

Answer: (D) 2