Question

The area of the region satisfying the inequalities $|x|-y≤1,y≥0$ and $y≤1$ is

Answer 1

The graph of $|x|-y≤1,y≥0$ and $y≤1$ is as follows:

Area of ABCD = Area of EFCD - Area of EAD - Area of BFC
= $EF×FC-\frac{1}{2}×EA×ED-\frac{1}{2}×BF×FC$
= $4×1-\frac{1}{2}×1×1-\frac{1}{2}×1×1$
= $4-1 = 3$ Square units