width to height formula for hexagon

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Is there a formula to calculate the height (a) of a regular hexagon when you know it's width (b)?

Is it possible to adapt this formula to a sum like :

b = a + a*x

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2 Answers

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Wikipedia article on hexagons states that a height-to-width ratio of a regular hexagon is 1:1.1547005.

So although trigonometry can do this, you can also use:

a = b * 0.8660254

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Draw a line from the centre to the upper left vertex. You now have a right angled triangle and some trigonometry will soon allow you to relate $a$ to $b$.

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