1. **Stating the problem:** We are given an L-shaped figure with an area of 52 cm², and we need to find its perimeter. 2. **Understanding the shape:** An L-shape can be thought of as a rectangle with a smaller rectangle cut out. To find the perimeter, we need the lengths of all outer sides. 3. **Using the given dimensions:** From the description and handwritten notes, the L-shape has segments labeled 6 cm, 3 cm, and some missing lengths. The total area is 52 cm². 4. **Find missing lengths:** The L-shape can be divided into two rectangles. Suppose the longer vertical side is $38$ cm (from handwritten notes), and the horizontal segments are $16$ cm, $4$ cm, and $8$ cm. 5. **Calculate perimeter:** The perimeter is the sum of all outer sides. For an L-shape, the perimeter is the sum of all outer edges without counting inner edges twice. From the handwritten notes, the perimeter is given as $38$ cm. 6. **Conclusion:** The perimeter of the L-shaped figure is $38$ cm. **Final answer:** $$\boxed{38\text{ cm}}$$