1. **Problem statement:** We have two similar shapes, S and T. Shape S has a perimeter of 12 cm and a height of 4 cm. Shape T has a height of 40 cm. We need to find the perimeter of shape T. 2. **Formula and rules:** For similar shapes, the ratio of their perimeters is equal to the ratio of their corresponding side lengths (or heights). This means: $$\frac{\text{Perimeter of T}}{\text{Perimeter of S}} = \frac{\text{Height of T}}{\text{Height of S}}$$ 3. **Substitute known values:** $$\frac{\text{Perimeter of T}}{12} = \frac{40}{4}$$ 4. **Simplify the ratio on the right:** $$\frac{40}{4} = 10$$ 5. **Solve for the perimeter of T:** $$\text{Perimeter of T} = 12 \times 10$$ 6. **Calculate the final answer:** $$\text{Perimeter of T} = 120 \text{ cm}$$ **Answer:** The perimeter of shape T is 120 cm.