Question

The area, in sq. units, enclosed by the lines $x=2$, $y=|x-2|+4$, the $X$-axis and the $Y$-axis is equal to

• A. 8
• B. 12
• C. 10
• D. 6

Answer 1

Answer: (C)

10

Answer 2

The line $y=|x-2|+4$ intersects the y -axis at $(0,6)$ and intersects $x=2$ at $(2,4)$
The other vertices are $(0,0)$ and $(2,0)$
The figure formed is a trapezium of parallel sides $6$ and $4$ and the distance between the parallel sides is $2$.
Required answer =$\frac{1}{2}×2×(6+4)=10$
So, the correct option is (C): $10$