To find the surface area of a prism, we need to find the area of each face and add them up.
Let's assume that the 9.4 mm length is the height of the prism and the 12 mm and 8 mm lengths are the base dimensions. The two bases are congruent, so we only need to find the area of one of them.
Area of base = length x width = 12 mm x 8 mm = 96 mm²
Now, let's find the area of each of the four lateral faces. Since the prism is rectangular, the lateral faces are all rectangles with height 9.4 mm. The lengths of the lateral faces are equal to the base dimensions.
Area of lateral face 1 = length x height = 12 mm x 9.4 mm = 112.8 mm²
Area of lateral face 2 = width x height = 8 mm x 9.4 mm = 75.2 mm²
Area of lateral face 3 = length x height = 12 mm x 9.4 mm = 112.8 mm²
Area of lateral face 4 = width x height = 8 mm x 9.4 mm = 75.2 mm²
Now, we can add up the areas of all the faces to get the total surface area of the prism:
Surface area = 2(base area) + 4(lateral face area) = 2(96 mm²) + 4(112.8 mm² + 75.2 mm²) = 2(96 mm²) + 4(188 mm²) = 2(96 mm²) + 752 mm² = 944 mm²
Therefore, the surface area of the given prism is 944 mm².