Hexagons's blog

By Hexagons, 3 years ago, In English

You are given a hexagon in which all his angles are equal in measure, you draw a circle inscribed inside the hexagon and tangent to the hexagon's sides, and another circle which is the circumscribed circle of the hexagon (all the hexagon vertices lie on the circumference of this circle), suppose the side length of the hexagon is $$$X$$$, find the area of the ring between the two circles in terms of $$$X$$$.

The ring in yellow is the required ring


BONUS : Find a general solution in terms of $$$N$$$ and $$$X$$$ (where polygon $$$P$$$ is a regular $$$N$$$th-gon of side length $$$X$$$ each) for the area of the ring between the circle inscribed in $$$P$$$ and the circle $$$P$$$ is inscribed in

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3 years ago, # |
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Use a normal font size like everyone else. It is like screaming. (It is rude.)

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    3 years ago, # ^ |
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    I thought it would fit for this relatively large photo, but Ok

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      3 years ago, # ^ |
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      Option 2: make the photo smaller?

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        3 years ago, # ^ |
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        Makes more sense, but I made that photo in the past and i was too lazy to edit it XD

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3 years ago, # |
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https://en.wikipedia.org/wiki/Regular_polygon#Circumradius

This should be all that you need. And the formula for the area of a circle on the radius.

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3 years ago, # |
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I mean I dont have a lot of trigonometry stuff , but I learned vectors here and there and I think since we know the side length of the polygon and each sides degree with the x axis , we can just do some vector addition like

1st vector is , length n , degree is 270 — 60

2nd vector is ,length n , degree is 60

1st vector + 2nd vector's = sqrt( (x1+x2)^2 + (y1 + y2)^2) that is the radius of the smaller circle

u can do the same with 3 vectors for finding the bigger circles radius I hope Im correct please fix me If Im wrong