8. (13 points) On the coordinate plane, all points whose coordinates satisfy the conditions

$$
\left\{\begin{array}{l}
|2 x+3 y|+|3 x-2 y| \leq 13 \\
2 x^{2}-3 x y-2 y^{2} \leq 0
\end{array}\right.
$$

are shaded. Find the area of the resulting figure.

#
# Answer: 13

Solution. The solution to the first inequality defines the square $ABCD$, the solution to the second inequality is the shaded part of the plane between the perpendicular lines $2x + y = 0$ and $x - 2y = 0$.

![](https://cdn.mathpix.com/cropped/2024_05_06_e78f4437465c0d87d859g-2.jpg?height=1010&width=1491&top_left_y=1391&top_left_x=294)