Asked by Ragu
A regular hexagon is to be cut from a sheet of diameter d.the width across corner is
Answers
Answered by
Reiny
I will assume that by "a sheet of diameter d"
you mean a circle.
Sketch 6 diameters, with a 60° angle between them.
sketch your hexagon and label the points A, B, C, D, E, and F
Not sure which line you want by "across corner"
But, ...
If you look at triangle ACE, you have a right-angled triangle,
since CE is a diameter. It is easy to see that this is also
a 30-60-90 triangle with ratios of sides of 1 : √3 : 2
So, depending which "across corner" side you want:
AE/d = 1/2, ---> AE = d/2
AC/d = √3/2 ---> AC = √3 d/2
you mean a circle.
Sketch 6 diameters, with a 60° angle between them.
sketch your hexagon and label the points A, B, C, D, E, and F
Not sure which line you want by "across corner"
But, ...
If you look at triangle ACE, you have a right-angled triangle,
since CE is a diameter. It is easy to see that this is also
a 30-60-90 triangle with ratios of sides of 1 : √3 : 2
So, depending which "across corner" side you want:
AE/d = 1/2, ---> AE = d/2
AC/d = √3/2 ---> AC = √3 d/2
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