Question 5 (Multiple Choice Worth 2 points)
(Types of Area MC)

A prism with a height of 12 millimeters has two regular hexagons for bases. The sides of the hexagon measure 7.5 millimeters, and the apothem of the hexagon measures 6.495 millimeters. What is the surface area of the prism?
$346.3 \mathrm{~mm}^{2}$
$686.1 \mathrm{~mm}^{2}$
$832.3 \mathrm{~mm}^{2}$
$1,124.6 \mathrm{~mm}^{2}$

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 \(\boxed{832.3 mm^2}\).