Because AB=BC=3, the triangle ABC is an isosceles triangle.

Because the angle ABC = 120, the angle BAF = 120 and BAC=30.

Ac = 2 * 3 * cos 30 can be solved.

Because AF=DE, angle AFE= angle DEF = 120, trapezoid AFED is an isosceles trapezoid, and because angle AFE = 120 and angle FAD=60, angle CAD=30, so CD = AC * Tan30 = 2 * 3 * Cos30.

In the isosceles trapezoid AFED, FE//AD and AF//EG make the quadrilateral AFEG into a parallelogram, so AF=EG=2, and because the angle DEG = 60 and ED=2, the triangle DEG is an equilateral triangle, so DG=2.

Ad = AC/cos 30 = 6, so AG=6-2=4, so EF=4.

finally

The circumference is 3+3+3+2+4+2= 17.