hexagon measurement
- Thread starter melidav
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- Apr 12, 2005
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45 years? What kind of measurement is that?! :lol:
You have stated that each side is 72". You have not stated that we are dealing with what is called a "Regular Hexagon". This would require that each outside angle measure 360º/6 = 60º. If this is the case, there is a unique answer.
If it's regular, your shape can be divided into 6 equilateral triangles. (connect the three pairs of opposite corners.) The height of these triangles is 1/2 the distance from parallel opposite sides. sin(60º)*72" = 72" * (sqrt(3)/2) = 62.354". So, the total distance between opposite parallels should be 2*62.354" = 124.708".
This actually gives a good way to check how "regular" it is. Measure the three pairs of opposite sides. If you get all three exactly 124.708", you did an excellent job! Note: 11/16 = 0.688 and 23/32 = 0.719
Getting into the gazebo business, are we?
You have stated that each side is 72". You have not stated that we are dealing with what is called a "Regular Hexagon". This would require that each outside angle measure 360º/6 = 60º. If this is the case, there is a unique answer.
If it's regular, your shape can be divided into 6 equilateral triangles. (connect the three pairs of opposite corners.) The height of these triangles is 1/2 the distance from parallel opposite sides. sin(60º)*72" = 72" * (sqrt(3)/2) = 62.354". So, the total distance between opposite parallels should be 2*62.354" = 124.708".
This actually gives a good way to check how "regular" it is. Measure the three pairs of opposite sides. If you get all three exactly 124.708", you did an excellent job! Note: 11/16 = 0.688 and 23/32 = 0.719
Getting into the gazebo business, are we?