8. (12 points) On the coordinate plane, all points whose coordinates satisfy the condition

$$
|| x|-2|+|y-3| \leq 3
$$

are shaded. Find the area of the resulting figure.
Answer: 34

Solution. The polygon that results from solving the equation ||$x|-2|+$ $|y-3|=3$ consists of segments of straight lines, glued together at special points: $x=0, x=2, x=$ $-2, y=3$.

![](https://cdn.mathpix.com/cropped/2024_05_06_c5ac26fa1d2ba726211fg-3.jpg?height=1011&width=1487&top_left_y=637&top_left_x=296)