SOLUTION: the perimeter of a hexagonal box measures 42m.what is the area?

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Question 176165: the perimeter of a hexagonal box measures 42m.what is the area?
Answer by solver91311(12126) About Me  (Show Source):
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If the perimeter of a regular hexagon is 42, each of the sides has length 42%2F6=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 %287%2Asqrt%283%29%29%2F2 (Use Pythagoras to verify) Therefore the area is %287%29%28%287%2Asqrt%283%29%29%2F2%29%281%2F2%29+=+%2849%2Asqrt%283%29%29%2F4. So the area of the hexagon is %28%2849%2Asqrt%283%29%29%2F4%29+%2A+6+=+%28147%2Asqrt%283%29%29%2F2 square meters.

Visit http://www.mathreference.com/geo,hex.html to see a picture.