Since all the triangles Stephan created have a height of 7 in and a base of 8 in, the surface area of the hexagonal prism is: B. 624 sq in.
Since there are six (6) congruent triangles in a hexagonal prism, we would determine the area of one of the triangles and then multiply by 6 as follows;
Area of triangle = 1/2 × base × height
Area of triangle = 1/2 × 7 × 8
Area of triangle = 28 square inches.
Area of hexagon = 6 × 28
Area of hexagon = 168 square inches.
Since there are two (2) hexagons in the net, we would multiply the area by 2 as follows;
Area of 2 hexagons = 2 × 168
Area of 2 hexagons = 336 square inches.
Note: Each rectangle has a side that is equal to one side of the hexagon and a side that is equal to the height of the prism.
For the rectangular sides of this hexagonal prism, we have;
Area of 6 rectangular sides = 6 × length × breadth
Area of 6 rectangular sides = 6 × 8 × 6
Area of 6 rectangular sides = 288 square inches.
Now, we can find the surface area of this hexagonal prism;
Surface area of hexagonal prism = 336 + 288
Surface area of the hexagonal prism = 624 square inches.