Let $ABCDEF$ be our regular hexagon, with centre $O$ - and join $AO, BO, CO, DO, EO,$ and $FO$. Note that we form six equilateral triangles with sidelength $\frac{s}{2}$, where $s$ is the sidelength of the triangle (since the perimeter of the two polygons are equal). If the area of the original equilateral triangle is $2$, then the area of each of the six smaller triangles is $1/4\times 2 = \frac{1}{2}$ (by similarity area ratios).
Thus, the area of the hexagon is $6\times \frac{1}{2}=3$, hence our answer is $\fbox{B}$