1. **Stating the problem:** We have a right triangle with base 6 cm, height 4 cm, and hypotenuse 5 cm, adjacent to a parallelogram with one side 5 cm (shared with the triangle) and another side 11 cm. We need to find the total surface area of the combined figure. 2. **Formula for area of a right triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Calculate the area of the triangle:** $$\text{Area}_{\triangle} = \frac{1}{2} \times 6 \times 4 = 12 \text{ cm}^2$$ 4. **Formula for area of a parallelogram:** $$\text{Area} = \text{base} \times \text{height}$$ 5. **Determine the height of the parallelogram:** Since the parallelogram shares the side of length 5 cm with the triangle, and the triangle's height is 4 cm, the height of the parallelogram is also 4 cm. 6. **Calculate the area of the parallelogram:** $$\text{Area}_{\text{parallelogram}} = 11 \times 4 = 44 \text{ cm}^2$$ 7. **Calculate the total surface area:** $$\text{Total Area} = \text{Area}_{\triangle} + \text{Area}_{\text{parallelogram}} = 12 + 44 = 56 \text{ cm}^2$$ **Final answer:** $$\boxed{56 \text{ cm}^2}$$