1. **State the problem:** We need to find the total surface area of a rectangular prism with dimensions given as $q$ cm (length), 4 cm (width), and 5 cm (height). Additionally, there is a triangular shape with height 4.6 cm on one side, which suggests the prism might have a triangular face instead of a rectangular one. 2. **Identify the shape and dimensions:** The prism has a rectangular base with sides $q$ cm and 4 cm. The height of the prism is 5 cm. The triangular face has a height of 4.6 cm, which likely corresponds to the slant height or a side face. 3. **Formula for total surface area of a prism:** For a prism with a triangular face and rectangular sides, the total surface area $A$ is the sum of the areas of all faces: $$A = 2 \times \text{area of base} + \text{perimeter of base} \times \text{height}$$ 4. **Calculate the area of the triangular base:** The base is a triangle with base $q$ cm and height 4 cm: $$\text{Area}_{\text{base}} = \frac{1}{2} \times q \times 4 = 2q$$ 5. **Calculate the perimeter of the triangular base:** The sides are $q$ cm, 4.6 cm, and 4 cm. So, $$P = q + 4.6 + 4 = q + 8.6$$ 6. **Calculate the lateral surface area:** Multiply the perimeter by the prism height 5 cm: $$\text{Lateral area} = (q + 8.6) \times 5 = 5q + 43$$ 7. **Calculate total surface area:** $$A = 2 \times 2q + 5q + 43 = 4q + 5q + 43 = 9q + 43$$ **Final answer:** $$\boxed{9q + 43 \text{ cm}^2}$$ This expression gives the total surface area in terms of $q$.