Let's denote the radius of the sector as $r$.
According to the problem, we have $l=\alpha r + 2r$
$4=2r+2r$
$r=1$
The area of the sector is $S_{\text{sector}}= \frac{1}{2}\alpha r^2= \frac{1}{2} \times 2 \times 1^2=1$.
Therefore, the answer is $\boxed{1}$.
To solve this problem, we first calculate the radius $r$ based on the circumference of the sector, and then use the formula for the area of a sector.
This question tests the application of the formula for the area and arc length of a sector under radian measure, and it is a basic problem.