4. As shown in Figure 9, the side length of square $A B C D$ is 10, and points $P$ and $Q$ are on the line segment connecting the midpoints of $A D$ and $B C$. Connecting $P A$, $P C$, $Q A$, and $Q C$, the square is divided into three parts of equal area. Find the length of line segment $P Q$.
4. $\frac{20}{3}$.

From the given, $S_{\square A P C Q}=\frac{100}{3}$.
Also, $S_{\square A P C Q}=S_{\triangle P Q C}+S_{\triangle P Q A}$ $=\frac{1}{2} P Q \times 10$,
thus $P Q=\frac{20}{3}$.