Answer
$$18+18\sqrt3$$
Work Step by Step
We see all of the sides of the squares have length 6. This means all of the triangles are isosceles triangles. We see that these base angles for the isosceles triangles are each 30 degrees using the size of angles for a hexagon. Thus, each isosceles triangle forms two right triangles. Since they are 30-60-90 triangles, each length is:
$$ =\frac{6}{2} \sqrt3 =3\sqrt3$$
There are 6 right triangles and 3 squares that form the perimeter, so the perimeter is:
$$ =6(3\sqrt3)+(6)(3) \\ = 18+18\sqrt3$$
