Question

The area enclosed within the curve |x| + |y| = 1

• A.
• B. 1
• C.
• D. 2

Answer 1

The correct option is D 2

The given lines are $\pm x\pm y=1$
i.e., x + y = 1, x – y = 1, x + y = – 1 and x – y = –1
These lines form a quadrilateral whose vertices are A(–1, 0), B(0, –1), C(1, 0) and D(0, 1)
Obviously ABCD is a square.
Length of each side of this square is $\sqrt{1^2+1^2}=\sqrt{2}$
Hence area of square is $\sqrt{2}\times \sqrt{2}=2sq.units$.
Trick: Required area = $\frac{2c^2}{|ab|}=\frac{2\times 1^2}{|1\times 1|}=2$.