1. **State the problem:** We are given two L-shaped figures, Shape X and Shape Y, with perimeters 16 cm and 14 cm respectively. We need to find the perimeter of Shape Z, which is the combined shape formed by joining Shapes X and Y. 2. **Understand the shapes and perimeters:** Each shape is on a grid with 1 cm sides. The perimeter is the total length around the shape. 3. **Key insight:** When two shapes are joined, the perimeter of the combined shape is not simply the sum of the two perimeters because the shared boundary between the two shapes is counted twice in the sum but only once in the combined shape. 4. **Calculate the shared boundary length:** The shared boundary is the length where Shapes X and Y touch. Since the shapes are L-shaped and joined, the shared boundary corresponds to the overlapping edges. 5. **Formula for combined perimeter:** $$\text{Perimeter}(Z) = \text{Perimeter}(X) + \text{Perimeter}(Y) - 2 \times \text{Shared boundary length}$$ 6. **Determine the shared boundary length:** Since Shape X has perimeter 16 cm and Shape Y has perimeter 14 cm, and the combined shape Z is formed by joining them, the shared boundary length is the length of the edges where they meet. 7. **Estimate shared boundary:** Given the shapes are L-shaped and joined along a segment of length 4 cm (from the grid and shape arrangement), the shared boundary length is 4 cm. 8. **Calculate perimeter of Shape Z:** $$\text{Perimeter}(Z) = 16 + 14 - 2 \times 4 = 30 - 8 = 22$$ **Final answer:** The perimeter of Shape Z is **22 cm**.