1. **State the problem:** We have three shapes X, Y, and Z on a 1 cm grid. - Perimeter of Shape X is 16 cm. - Perimeter of Shape Y is 14 cm. - Shape Z is formed by combining Shapes X and Y. We need to find the perimeter of Shape Z. 2. **Understand the shapes:** Shape Z encloses both X and Y combined. Since X and Y are placed such that Y fits below X, some edges are shared and do not contribute to the perimeter of Z. 3. **Calculate the perimeter of Z:** - The perimeter of Z equals the sum of the perimeters of X and Y minus twice the length of the shared boundary (because shared edges are counted twice in X and Y but only once in Z). - Let the length of the shared boundary be $s$ cm. - Then, $$\text{Perimeter of Z} = 16 + 14 - 2s = 30 - 2s.$$ 4. **Find the shared boundary length $s$:** - Since the shapes fit exactly along the grid lines, the shared boundary corresponds to the length where Y touches X. - By examining the grid and the shapes, the shared boundary length is 6 cm. 5. **Calculate the perimeter of Z:** $$\text{Perimeter of Z} = 30 - 2 \times 6 = 30 - 12 = 18 \text{ cm}.$$ **Final answer:** The perimeter of Shape Z is **18 cm**.