The perimeter of the hexagon ACEFGH is calculated by adding the lengths of its sides.
Each trapezoid is congruent to trapezoid ABCD (All sides of each trapezoid have the same lengths to the sides of the trapezoid ABCD) so the lengths can be known:
Length AH = 4 cm + 6 cm = 10 cm
Length AC = 3 cm
Length CE = 3 cm
Length EF = 4 cm + 6 cm = 10 cm
Length FG = 3 cm
Length GH = 3 cm
The perimeter of hexagon ACEFGH is:
Perimeter = 10 cm + 3 cm + 3 cm + 10 cm + 3 cm + 3 cm
Perimeter = 32 cm