To find the perimeter of the composite figure in the image, we need to add up the lengths of all the outer sides.

Known Measurements from the Diagram:

1. Top horizontal line: 9 cm
2. Top right vertical line: 4 cm
3. Right middle vertical lines: 6 cm (two segments)
4. Right bottom vertical line: 5 cm
5. Left vertical line: 14 cm
6. Bottom horizontal line: Not explicitly given but can be inferred from other lengths. It should be $9 - 5 = 4$ cm.

Now, let's list the sides step by step:

• Left vertical side: 14 cm
• Top horizontal side: 9 cm
• Top right vertical side: 4 cm
• Two middle right vertical sides: 6 cm + 6 cm
• Bottom right vertical side: 5 cm
• Bottom horizontal side: 4 cm

Summing up the lengths:

$\text{Perimeter} = 14 + 9 + 4 + 6 + 6 + 5 + 4 + (the height difference between the left and right verticals)$