Question 1205543: Hello
It was explained to me that for a regular hexagon
the parrallel height from edge (a) to edge (a) is 2 over root 3.
For a regular hexagon of sides a = 1
How do you prove the side to side dimension is equal to (2 over root3)?
sides a = 1
h= 2Ri
Where Ri = (Root3 over 2)x a
When I substitute (Root 3 over 2) x a into the formula for h
I get, 2(root 3 over 2) x a
Where a = 1
How do I transpose the formula to prove
h = 2 over root 3 ?
Your advice would be much appreciated.
Kind Regards
HayesD
Resources for formulae
https://calcresource.com/geom-hexagon.html
https://calckit.io/tool/geometry-hexagon
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
When the side length of the regular hexagon is 1, the distance between parallel sides of the hexagon is NOT 2/sqrt(3).
The distance, as you have found, is 2(sqrt(3)/2) = sqrt(3).
Picture the regular hexagon as being composed of 6 equilateral triangles.
Draw a line connecting opposite sides of the hexagon, dividing 2 of those equilateral triangles each into two 30-60-90 right triangles. In those right triangles, the short leg is 1/2, so the long leg is sqrt(3)/2; and the distance between the opposite sides of the hexagon is twice that, which is sqrt(3).
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
It was explained to me that for a regular hexagon
the parrallel height from edge (a) to edge (a) is 2 over root 3.
~~~~~~~~~~~~~~~~~~~~~
What was explained to you, was INCORRECT.
The term "the parrallel height", used in your post, is incorrect, too.
|
|
|
