1. **Problem statement:** Find the surface area of the parallelogram prism with base sides 7 mm and 5 mm, height 4 mm, and an additional right triangle height 3 mm. 2. **Formula for surface area of a prism:** $$\text{Surface Area} = 2 \times \text{Base Area} + \text{Perimeter of base} \times \text{Prism height}$$ 3. **Calculate the base area:** The base is a parallelogram with sides 7 mm and 5 mm and height 4 mm. $$\text{Base Area} = \text{base} \times \text{height} = 7 \times 4 = 28 \text{ mm}^2$$ 4. **Calculate the perimeter of the base:** $$\text{Perimeter} = 2 \times (7 + 5) = 2 \times 12 = 24 \text{ mm}$$ 5. **Determine the prism height:** The prism height is given by the right triangle height 3 mm. 6. **Calculate the lateral surface area:** $$\text{Lateral Surface Area} = \text{Perimeter} \times \text{Prism height} = 24 \times 3 = 72 \text{ mm}^2$$ 7. **Calculate total surface area:** $$\text{Surface Area} = 2 \times 28 + 72 = 56 + 72 = 128 \text{ mm}^2$$ **Final answer:** The surface area of the parallelogram prism is **128 mm\textsuperscript{2}**.