How can I calculate the area of a hexagon which all of it's angles are equal given 3 of it's sides?
Edit:
I forgot the constraint that opposite sides have same length, e.g. for hexagon $ABCDEF$
$AB = DE$
$BC = EF$
$CD = FA$
Calculating the area of a special hexagon
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$\begingroup$
geometry
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0@Mark Bennet: you are right, I forgot a constraint, see the edit. – 2011-08-31
2 Answers
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As Mark already explained, you can not find the area of a hexagon with only the length of three of its sides and all the angles known.
Formulae for the area, perimeter, and other interesting facts about hexagons can be found on the Wikipedia page.
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0See the first computation [here](http://math.stackexchange.com/a/673018/120249). It provides a nice direct way to calculate these areas. – 2014-02-27
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Given your constraints, opposite sides of the hexagon are parallel. You can draw diagonals $AF$ and $BD$, which are also parallel and equal and $AD$. The length of $AF$ and $BD$ can be found from the law of cosines and the area of the triangles from Heron's formula (among other ways.) Then the angles can be assessed to determine $AD$ and the area of the other two triangles.