Question

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?

1) 346.3 mm²
2) 686.1 mm²
3) 832.3 mm²
4) 1,124.6 mm²

Answer 1

The surface area of the prism is 346.3 mm².

Step-by-step explanation:

To find the surface area of the prism, we need to find the areas of the two hexagon bases and the lateral faces.

The area of a regular hexagon can be found using the formula: Area = (3√3 × side^2) / 2.

Given that the side length of the hexagon is 7.5 mm, we can substitute this value into the formula to find the area.

The area of each hexagon base is: (3√3 × (7.5)^2) / 2 = 97.3125 mm².

The lateral faces of the prism are rectangles with dimensions equal to the side length of the hexagon and the height of the prism.

Therefore, the total surface area of the prism is: 2(area of hexagon base) + (perimeter of hexagon base × height) = 2(97.3125 mm²) + (6(7.5 mm) × 12 mm) = 346.3 mm².