1. **State the problem:** We need to find the surface area of a triangular prism with given dimensions. 2. **Identify the dimensions:** - Triangular base: base $b=4$ m, height $h=3$ m - Length (depth) of prism $L=7$ m - Additional rectangle face dimensions given as height $12$ m and width $5$ m, but these do not correspond to the prism's faces based on the triangular base and length. 3. **Formula for surface area of a triangular prism:** $$\text{Surface Area} = 2 \times \text{Area of triangular base} + \text{Perimeter of triangular base} \times \text{Length}$$ 4. **Calculate the area of the triangular base:** $$\text{Area} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 4 \times 3 = 6 \text{ m}^2$$ 5. **Find the lengths of the sides of the triangular base:** - Base side $=4$ m - Height side $=3$ m - Hypotenuse side $= \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$ m 6. **Calculate the perimeter of the triangular base:** $$P = 4 + 3 + 5 = 12 \text{ m}$$ 7. **Calculate the lateral surface area:** $$\text{Lateral Surface Area} = P \times L = 12 \times 7 = 84 \text{ m}^2$$ 8. **Calculate total surface area:** $$\text{Surface Area} = 2 \times 6 + 84 = 12 + 84 = 96 \text{ m}^2$$ **Final answer:** The surface area of the triangular prism is $96$ square meters.