Dividing a Hexagon into 8 Equal Parts
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.
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/
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