Question

The area bounded by the curves \(y=|x|\) and \(y=4-|x|\) is ..... sq units.

• A. \(4\)
• B. \(8\)
• C. \(4\sqrt{2}\)
• D. \(16\)

Hint:

Find the intersection points and use symmetry about the Y-axis.

Answer 1

The Correct Option is B

Step 1: Recognise the Shape
The lines $y=|x|$ and $y=4-|x|$ form a square with vertices $(0,0)$, $(2,2)$, $(0,4)$, $(-2,2)$.

Step 2: Side Length
The side from $(0,0)$ to $(2,2)$ is $2\sqrt{2}$.

Step 3: Area
Area $=(2\sqrt{2})^{2}=8$ square units.

Final Answer:
The square formed has area 8. \[ \boxed{\text{(B) }8} \]