SOLUTION: What is the surface area of a hexagonal prism with an apothem of 3 a height of 4 and a side being 2

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Question 868046: What is the surface area of a hexagonal prism with an apothem of 3 a height of 4 and a side being 2
Answer by KMST(5328) About Me  (Show Source):
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Apothem is defined for regular polygons as the distance from a side to the center of the polygon.
A regular hexagon with a side of 2 has an apothem of sqrt%283%29= approximately 1.732 . It could not have an apothem of 3 .

For a regular polygon, the area can be calculated as %28perimeter%29%28apothem%29%2F2 .
A hexagon with a side of 2 has a perimeter of %286%29%282%29=12
and a surface area of approximately 12%281.732%29%2F2=10.392 .
The lateral area of a right prism can be calculated as %28perimeter%29%28height%29 .
A hexagonal base prism with a perimeter of 12 and a height of 4
has a lateral area of 12%284%29=48 .
Adding that lateral area plus the area of the two hexagonal bases, we get a total area of
48%2B2%2810.392%29=48%2B10.784=68.784 .