Question 176165
If the perimeter of a regular hexagon is 42, each of the sides has length {{{42/6=7}}}.  A regular hexagon consists of six congruent equilateral triangles, each having side lengths equal to the side of the hexagon.  An equilateral triangle with side lengths of 7 has a base of 7 and a height of {{{(7*sqrt(3))/2}}} (Use Pythagoras to verify)  Therefore the area is {{{(7)((7*sqrt(3))/2)(1/2) = (49*sqrt(3))/4}}}.  So the area of the hexagon is {{{((49*sqrt(3))/4) * 6 = (147*sqrt(3))/2}}} square meters.


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