4. Find the area of the region $\left\{(x, y) \in \mathbb{R}^{2}:|x|-|y| \leq 2\right.$ and $\left.|y| \leq 2\right\}$.
Answer: 24 sq. units
Solution: In the first quadrant, the region is a trapezoid with vertices at $(4,2),(2,0),(0,0),(0,2)$; this trapezoid has area 6 . By symmetry, the region has area $4 \times 6=24$ square units.