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### Dividing a Hexagon into 8 Equal Parts

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Date: 06/11/99 at 02:02:34
From: Stef
Subject: Dividing a hexagon into 8 equal parts

How do you divide a hexagon into 8 equal parts? I figured out how to
divide it into 4 equal trapezoids but I have to figure out how to
divide it into 8 equal parts.
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Date: 06/11/99 at 05:56:39
From: Doctor Pete
Subject: Re: Dividing a hexagon into 8 equal parts

Hi,

I assume by "hexagon" you mean "regular hexagon," with all sides equal
and all interior angles equal. A novel way to dissect it into 8
congruent parts is as follows:

Suppose you have the vertices labeled A, B, C, D, E and F in clockwise
order. Let O be the center of the hexagon ABCDEF. Draw regular hexagon
A'B'C'D'E'F' such that it also has center O, and A'B' is parallel to
AB, B'C' is parallel to BC, etc., and furthermore, A'D' is half of AD.
Then draw lines AA', BB', CC', DD', EE', FF', and draw line A'D'. This
divides the original hexagon into 8 congruent trapezoids.

Now, here's a question for you: How many different ways can you divide
the same hexagon up into 8 congruent trapezoids like the ones you
found in the above example? (Hint: Take the trapezoids you found in
the example and divide each up into three equilateral triangles.)

- Doctor Pete, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons

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