jmc

Let the perimeter of the equilateral triangle be $3s$. The side length of the equilateral triangle would then be $s$ and the sidelength of the hexagon would be $\frac{s}{2}$. A hexagon contains six equilateral triangles. One of these triangles would be similar to the large equilateral triangle in the ratio $1:4$, since the sidelength of the small equilateral triangle is half the sidelength of the large one. Thus, the area of one of the small equilateral triangles is $1$. The area of the hexagon is then $1\times 6=\boxed{6}$.