Question

The area enclosed by the graphs of |x+y|=2 and |x|=1 is:

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is D 8

$|x+y|=2$

$\Rightarrow x+y=\pm 2$

$\left|x\right|=1$

$\Rightarrow x=\pm 1$

From the fig., attached, the resultant fig., is a parallelogram having vertices $(-1,3),(1,1),(1,3)$ and $(-1,-1)$.

Therefore,

$BP=2$ units

$BC=4$ units

Therefore,Area of parallelogram $ABCD=BP\times BC=2\times 4=8$ sq. units.

Hence the correct answer is $\left(D\right)8$.