4. Let $O$ be the incenter of $\triangle A B C$, $A B=5, A C=6, B C=7, O P=x O A+y O B+z O C$, $0 \leq x, y, z \leq 1$, then the area of the plane region covered by the trajectory of the moving point $P$ is equal to
4. $12 \sqrt{6}$.

Analysis: As shown in the right figure, according to the geometric meaning of vector addition, point $P$ moves within the three parallelograms and their interiors in the figure. Therefore, the area of the plane region covered by the trajectory of moving point $P$ is equal to twice the area of $\triangle A B C$, which is $12 \sqrt{6}$.