Step 1 :Calculate the perimeter of the base, which is a regular hexagon. The perimeter of a hexagon is given by the formula \(Perimeter = 6 \times side\). So, the perimeter of our hexagon is \(6 \times 7.5 mm = 45 mm\).
Step 2 :Calculate the area of the base using the formula \(Area = \frac{1}{2} \times Perimeter \times Apothem\). So, the area of the base is \(\frac{1}{2} \times 45 mm \times 6.495 mm = 146.1375 mm^2\).
Step 3 :Calculate the lateral area of the prism, which is the perimeter of the base times the height. This gives us \(45 mm \times 12 mm = 540 mm^2\).
Step 4 :Add the areas together to find the total surface area of the prism. The surface area is given by the formula \(Surface Area = 2 \times (Area of Base) + Lateral Area\). So, the surface area of the prism is \(2 \times 146.1375 mm^2 + 540 mm^2 = 832.275 mm^2\).
Step 5 :Round the final answer to one decimal place. So, the surface area of the prism is \(\boxed{832.3 mm^2}\).