1. **Problem Statement:** Calculate the surface area of a triangular prism with given side lengths of the triangular base and the prism height. 2. **Formula:** The surface area $SA$ of a triangular prism is given by: $$SA = 2 \times \text{Area of triangular base} + \text{Perimeter of base} \times \text{Height of prism}$$ 3. **Step 1: Identify dimensions** - Triangular base sides: 7.3 cm, 7 cm, 4 cm - Prism height (length): 12 cm 4. **Step 2: Calculate the area of the triangular base using Heron's formula** - Semi-perimeter $s = \frac{7.3 + 7 + 4}{2} = \frac{18.3}{2} = 9.15$ cm - Area $A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{9.15(9.15-7.3)(9.15-7)(9.15-4)}$ 5. **Step 3: Calculate inside the square root** $$9.15 - 7.3 = 1.85$$ $$9.15 - 7 = 2.15$$ $$9.15 - 4 = 5.15$$ 6. **Step 4: Calculate the product** $$9.15 \times 1.85 \times 2.15 \times 5.15 = 187.07$$ 7. **Step 5: Calculate the area** $$A = \sqrt{187.07} \approx 13.68 \text{ cm}^2$$ 8. **Step 6: Calculate the perimeter of the base** $$P = 7.3 + 7 + 4 = 18.3 \text{ cm}$$ 9. **Step 7: Calculate the surface area** $$SA = 2 \times 13.68 + 18.3 \times 12 = 27.36 + 219.6 = 246.96 \text{ cm}^2$$ 10. **Final answer:** The surface area of the triangular prism is approximately **246.96 cm²**.