4. The area of the figure enclosed by the curve determined by the equation $|x-1|+|y-1|=1$ is
A. 1
B. 2
C. $\pi$
D. 4
Answer
As shown in the figure, consider four points $A(1,0), B(0,1), C(1,2), D(2,1)$, then the curve sought is the square $A B C D$. It is easy to know that its side length is $\sqrt{2}$, and the area is 2. Therefore, the answer is $B$.