1. **State the problem:** We need to find the surface area of a triangular prism with a triangular base having sides 5, 5, and base 6 units, height of the triangle 4 units, and prism length 7 units. 2. **Formula for surface area of a triangular prism:** $$\text{Surface Area} = 2 \times \text{Area of triangular base} + \text{Perimeter of base} \times \text{Length of prism}$$ 3. **Calculate the area of the triangular base:** The base is a triangle with base $b=6$ and height $h=4$. $$\text{Area} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 6 \times 4 = 12$$ 4. **Calculate the perimeter of the triangular base:** The sides are 5, 5, and 6. $$\text{Perimeter} = 5 + 5 + 6 = 16$$ 5. **Calculate the lateral surface area:** $$\text{Lateral Surface Area} = \text{Perimeter} \times \text{Length} = 16 \times 7 = 112$$ 6. **Calculate total surface area:** $$\text{Surface Area} = 2 \times 12 + 112 = 24 + 112 = 136$$ **Final answer:** The surface area of the triangular prism is $136$ square units.