Solution: extend AB, CD and EF edges in two directions respectively. Let AB and CD meet M, CD and EF meet N, AB and EF meet L. 。

From the fact that all six angles of the convex hexagon ABCDEF are 120 degrees, we can get: ∠ LAF = ∠ LFA = 60 degrees.

That is, alf =180-2× 60 = 60.

So the triangle ALF is an equilateral triangle.

Similarly, triangle CDM and triangle DEN are equilateral triangles.

And < cmd = < dne = 60.

Triangle LMN is also an equilateral triangle.

LM=LN=MN=8+ 1 1+6=25

Easy to get: AF = Al = 25-8-2 = 15, EF = LN-LF-EN = 25- 15-6 = 4.

So the perimeter is 2+8+11+6+15+4 = 46.