document.write( "Question 176165: the perimeter of a hexagonal box measures 42m.what is the area? \n" ); document.write( "

Algebra.Com's Answer #131250 by solver91311(24713) $\"\"$ $\"About$

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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.\r
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