Let the sector radius be R arc length L central angle A (radian).

2r+l =6 because the circumference =6.

(1/2) RL with an area of 2 = 2.

Combining the above two equations, we can get r= 1 L=4 (omitted, because when L=4, the arc of the sector is longer than one week, and one week is π.

a=L/r =2/2= 1

The radian number of the central angle is 1 radian.