SOLUTION: Let IJKLMN be a hexagon with side lengths IJ = LM = 2, JK = MN = 2, and KL = NI = 2. Also, all the interior angles of the hexagon are equal. Find the area of hexagon IJKLMN.

Algebra ->  Geometry-proofs -> SOLUTION: Let IJKLMN be a hexagon with side lengths IJ = LM = 2, JK = MN = 2, and KL = NI = 2. Also, all the interior angles of the hexagon are equal. Find the area of hexagon IJKLMN.      Log On


   

Question 1210524: Let IJKLMN be a hexagon with side lengths IJ = LM = 2, JK = MN = 2, and KL = NI = 2. Also, all the interior angles of the hexagon are equal. Find the area of hexagon IJKLMN.
Answer by ikleyn(53646) About Me  (Show Source):
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Let IJKLMN be a hexagon with side lengths IJ = LM = 2, JK = MN = 2, and KL = NI = 2.
Also, all the interior angles of the hexagon are equal. Find the area of hexagon IJKLMN.
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From the problem, all 6 sides have the same length of 2 units,
and all interior angles are equal.


So, we have a regular hexagon.


Its area is 6 times the area of the equilateral central triangle with the side length of 2 units.


So, the answer to the problem is  6%2Aa%5E2%2A%28sqrt%283%29%2F4%29 = 6%2A2%5E2%2Asqrt%283%29%2F4%29 = 6%2Asqrt%283%29 = 10.3923 square units, approximately.

Solved.