Question

Find the area bounded by the curves $|x + y| = 1$, $|x| = 1$, $|y| = 1$.

• A. 4
• B. 3
• C. 2
• D. 1

Hint:

Break symmetric regions into basic shapes to calculate areas quickly.

Answer 1

The Correct Option is C

$|x+y|=1$ are two parallel lines $x+y=1$ and $x+y=-1$. $|x|=1$ and $|y|=1$ define a square of side 2 centred at origin. The strip between $x+y=\pm 1$ inside the square is a symmetric region. Area of strip = square area (4) minus two congruent right triangles each of area 1. So area = $4 - 2 \times 1 = 2$. \[ \boxed{2} \]