5. Find the area of a geometric figure, the coordinates of the vertices of which are the solutions to the system of equations

$$
\left\{\begin{array}{l}
x^{4}+\frac{7}{2} x^{2} y+2 y^{3}=0 \\
4 x^{2}+7 x y+2 y^{3}=0
\end{array}\right.
$$
# Solution:

The system of equations has only three real solutions: $(0 ; 0),(2 ;-1),\left(-\frac{11}{2} ;-\frac{11}{2}\right)$. The area of the triangle with vertices at these coordinates is $16 \frac{1}{2}$.

Answer: $16 \frac{1}{2}$