Posted by Geomtery on Tuesday, February 21, 2012 at 10:11pm.
The polygon can be divided up into six triangles, each with base=s and height=6
Since it is a hexagon, you know the triangles are equilateral triangles, with height (apothem) = s*sqrt(3)/2
So, if the apothem is 6, 6 = s*sqrt(3)/2, and s = 12/sqrt(3) = 4sqrt(3)
A = 1/2 * a * p
= 1/2 * 6 * 6*4sqrt(3)
= 72sqrt(3)
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