Answer:
Surface area of prism A is approximately 12.4 square units.
Explanation:
Since prism A and prism B are similar, their corresponding side lengths are proportional. Let's use the scale factor k to represent the ratio of the side lengths of prism B to those of prism A. Then, the volume of prism B is (k³)(27) = 27k³ cubic units. Similarly, the surface area of prism B is (k²)(surface area of prism A).
We are given that the volume of prism B is approximately 512 cubic units. Therefore, we can solve for k:
27k³ = 512
k³ = 512/27
k ≈ 3.62
Now, we can use k to find the surface area of prism A:
surface area of prism B = (k²)(surface area of prism A)
128 = (3.62²)(surface area of prism A)
surface area of prism A ≈ 12.4 square units
Therefore, the surface area of prism A is approximately 12.4 square units.