The surface area is the perimeter of the base multiplied by the
height added to twice of the area of the base
SA = P*h +
2B
We'll calculate the perimeter of the
base:
p = 6*l, where l = 9 cm
P =
6*9
P = 54 cm
We'll multiply the
perimeter by the height:
P*h = 54 cm*12 cm = 648
cm^2
Now, we'll calculate the area of the
base:
B = 3*l^2*sqrt3/2
l = 9
cm
B = 3*81*sqrt3/2
B =
121.5*sqrt3
2B= 2*121.5*sqrt3
2B =
243*sqrt3
Now, we'll gather all the results and we'll compute the
surface area of the hexagonal prism:
SA = 648 +
243*sqrt3
SA = 1068.39
cm^2
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