8. In the complex plane, the point corresponding to the complex number $z_{1}$ moves on the line segment connecting 1 and $\mathrm{i}$, and the point corresponding to the complex number $z_{2}$ moves on the circle centered at the origin with a radius of 1. Then the area of the region where the point corresponding to the complex number $z_{1}+z_{2}$ is located is $\qquad$ . .
8. $2 \sqrt{2}+\pi$.

Let $z_{1}=t+\mathrm{i}(1-t)(0 \leqslant t \leqslant 1)$,
$z_{2}=\cos \theta+\mathrm{i} \sin \theta$.
Then $z_{1}+z_{2}=x+y \mathrm{i}$
$$
=t+\cos \theta+\mathrm{i}(1-t+\sin \theta) \text {. }
$$

Therefore, $(x-t)^{2}+[y-(1-t)]^{2}=1$ represents a set of circles with centers on the line $y=1-x$, and the area of this region is $2 \sqrt{2}+\pi$.