Final answer:
The surface area of the triangular prism is calculated by summing the areas of its two triangular bases and three rectangular sides. The correct total surface area for the given measurements of the prism is 552 mm².
Step-by-step explanation:
The question pertains to finding the surface area of a triangular prism. To find the surface area of a triangular prism, we add together the areas of the two triangular bases and the areas of the three rectangular sides. The area of a triangle can be found using the formula Area = 1/2 × base × height. Given that one triangular base has a base of 16 mm and a height of 12 mm, its area is 1/2 × 16 × 12 = 96 mm². Since there are two triangular bases, we double this area to get both triangular areas combined.
Next, the area of one rectangular side face of the prism (with a base of 12 mm and a height of 10 mm) is base × height = 12 × 10 = 120 mm². A triangular prism has three of these rectangular faces. Adding the areas together:
- Area of triangular bases: 96 mm² × 2 = 192 mm²
- Area of one rectangular side: 120 mm²
- Area of three rectangular sides: 120 mm² × 3 = 360 mm²
Finally, by adding the area of the triangular bases and the rectangular sides, we get the total surface area of the prism:
192 mm² + 360 mm² = 552 mm²
Therefore, the correct surface area of the prism is 552 mm², which suggests that the provided answer choices are incorrect.