7. In the tetrahedron $P-ABC$,
$$
AB=\sqrt{3}, AC=1, PB=PC=\sqrt{2} \text{.}
$$

Then the range of $S_{\triangle ABC}^{2}+S_{\triangle PBC}^{2}$ is
7. $\left(\frac{1}{4}, \frac{7}{4}\right)$.

Reflect $\triangle P B C$ to be coplanar with $\triangle A B C$. Consider quadrilateral PBAC.

Obviously, when $B C=2$, $S_{\triangle A B C}^{2}+S_{\triangle P B C}^{2}$ reaches the maximum value $\frac{7}{4}$; when $A$, $B$, and $C$ are collinear, $S_{\triangle A B C}^{2}+S_{\triangle P B C}^{2}$ reaches the minimum value $\frac{1}{4}$.