1. **State the problem:** Find the surface area of a triangular prism with given dimensions: triangle base sides 10 m, 10 m, and 6 m, and prism length 16 m. 2. **Formula:** Surface area of a triangular prism = 2 × (area of triangular base) + (perimeter of base) × (length of prism). 3. **Calculate the area of the triangular base:** Use Heron's formula. - Semi-perimeter $s = \frac{10 + 10 + 6}{2} = 13$ m. - Area $= \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{13(13 - 10)(13 - 10)(13 - 6)} = \sqrt{13 \times 3 \times 3 \times 7} = \sqrt{819}$. - Simplify $\sqrt{819} \approx 28.62$ m$^2$. 4. **Calculate the perimeter of the triangular base:** $10 + 10 + 6 = 26$ m. 5. **Calculate the lateral surface area:** Perimeter × length = $26 \times 16 = 416$ m$^2$. 6. **Calculate total surface area:** $$\text{Surface area} = 2 \times 28.62 + 416 = 57.24 + 416 = 473.24 \text{ m}^2.$$