CAT 2020 Slot 1 QA Question 12: The area of the region satisfying the inequalities $|x| - y \leq 1$, $y \geq 0$ and $y \leq 1$ is

Question

The area of the region satisfying the inequalities $|x| - y \leq 1$, $y \geq 0$ and $y \leq 1$ is

Accepted Answer

The inequalities $y \geq 0$ and $y \leq 1$ restrict $y$ to the strip from 0 to 1.

$|x| - y \leq 1$
$\Rightarrow |x| \leq y + 1$
$\Rightarrow -(y + 1) \leq x \leq y + 1$

At $y = 0$, the horizontal length is 2. At $y = 1$, the horizontal length is 4.

So, the required region is a trapezium of height

The area of the region satisfying the inequalities ∣x∣−y≤1|x| - y \leq 1∣x∣−y≤1, y≥0y \geq 0y≥0 and y≤1y \leq 1y≤1 is