Question

The area of the region bounded by the curves $y=|x-2|$ and $y=4-|x|is-$

• A. 2
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is D 6

From the attached fig., $ABCD$ is the region bounded by the curves $y=|x-2|$ and $y=4-\left|x\right|$.

Since $ABCD$ is a rectangle, therefore

$ar\left(ABCD\right)=$ area of rectangle $=AB\times BC$

Now,

$AB=\sqrt{{(-1-0)}^2+{(4-3)}^2}=\sqrt{2}$

$BC=\sqrt{{(3-0)}^2+{(1-4)}^2}=3\sqrt{2}$

$\therefore ar\left(ABCD\right)=\sqrt{2}\times 3\sqrt{2}=6\text{sq. units}$

Hence the area of region bounded by the curves $y=|x-2|$ and $y=4-\left|x\right|$ is $6$ units.