Question

A regular hexagon is to be cut from a sheet of diameter D The width across corner

Answer 1

Answer:

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

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