8. The robot, based on the command, can complete at most the following two steps on a plane: First, it walks from the origin $O$ in a direction that is $\alpha$ $\left(0^{\square} \leq \alpha \leq 90^{\square}\right)$ degrees northeast for a period of time, then it walks north for a period of time, but the time to change direction is uncertain. Assuming the robot's walking speed is 10 meters per minute, the possible range of the robot's position after walking for 2 minutes is $\qquad$ square meters.
8. $25 \pi-50$

Analysis: It is easy to know that the area formed by the position is a segment, i.e., the area should be one quarter of the area of a circle minus the area of an isosceles right triangle, so the area should be $25 \pi-50$.