width to height formula for hexagon

Question

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

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

b = a + a*x

The half-height $a/2$ and the half-width $b/2$ are the altitude and base of an equilateral triangle. The ratio between these is $b/a=2/\sqrt{3}$. So $b=2a/\sqrt{3}=a+a\cdot(2\sqrt{3}-3)/3$. — mjqxxxx, May 15 '14 at 16:50

score 3 · Answer 1 · answered Aug 19 '19 at 19:58

3

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

answered Aug 19 '19 at 19:58

John

131

how is it calculated that number? – nkint Jan 03 '21 at 14:52
@nkint In the parameters section of the Wikipedia page, it notes that d = sqrt(3) / 2 * D. In this context d is the value called a in the OP's post, and D is the value called b. If you evaluate sqrt(3) / 2 it comes out to 0.8660254 – dgnuff Jan 27 '22 at 19:59

score 2 · Accepted Answer · answered May 15 '14 at 16:47

2

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 $b$.

answered May 15 '14 at 16:47

john

5,633

More so trigonometry, as you know the angles in a regular hexagon. – john May 15 '14 at 16:57

width to height formula for hexagon

2 Answers2