5. Find the area of the polygon, the coordinates of the vertices of which are the solutions of 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: $16 \frac{1}{2}$