6. Let $O$ be the incenter of $\triangle A B C$,
$$
\begin{array}{l}
A B=3, A C=4, B C=5, \\
\overrightarrow{O P}=x \overrightarrow{O A}+y \overrightarrow{O B}+z \overrightarrow{O C}, \\
0 \leqslant x, y, z \leqslant 1 .
\end{array}
$$

Then the area of the plane region covered by the moving point $P$ is equal to . $\qquad$
6. 12 .

As shown in Figure 2, according to the geometric meaning of vector addition, point $P$ moves within the three parallelograms and their interiors. Therefore, the area of the plane region covered by the trajectory of the moving point $P$ is equal to twice the area of $\triangle A B C$, which is 12.