105 The set of points $\{(x, y)|||x|-1|+| y |=\boldsymbol{z}\}$ forms a closed broken line, and the area enclosed by this closed broken line is
A. 14
B. 16
C. 18
D. 20
105 A. ||$x|-1|+|y|=2$ when $x \geqslant 1, y \geqslant 0$, it becomes $x+y=3$; when $0 \leqslant x \leqslant 1, y \geqslant 0$, it becomes $x-y=3$. By making symmetry about the $x$-axis and $y$-axis, we can obtain the other parts, as shown in Figure 2:

The area in the first quadrant is $\frac{1}{2} \times 2 \times 2+\frac{1}{2}(1+2) \times 1=\frac{7}{2}$. The total area is $4 \times \frac{7}{2}=14$.