# Dividing a hexagon into 12 congruent parts

• Nov 5th 2008, 02:57 PM
marspatrol
Dividing a hexagon into 12 congruent parts
I need help on a project. Here is the problem : Dissecting a Hexagon
Draw 6 regular hexagons. Then dissect each hexagon into twelve identical or congruent parts in 6 different ways. Note: A regular hexagon has 6 equal angle and 6 equal sides.
Also, my teacher told me that one of them involved squares, but I can't figure that one out. Please help. I already have these: http://i116.photobucket.com/albums/o...atrol/fgfg.jpg
• Nov 5th 2008, 03:58 PM
pyromir
1 answer is to make 2 triangle one going<|and the other |>. they would be intersecting each otherto create a 6 pointed star
• Nov 5th 2008, 04:03 PM
marspatrol
Quote:

Originally Posted by pyromir
1 answer is to make 2 triangle one going<|and the other |>. they would be intersecting each otherto create a 6 pointed star

That is not congruent/equal, but thanks anyways.
• Jan 22nd 2014, 07:30 AM
chopinwaltzes1737
Re: Dividing a hexagon into 12 congruent parts
Attachment 30063Attachment 30063

There are many different ways, these are just some of them.
• Jan 22nd 2014, 02:52 PM
Soroban
Re: Dividing a hexagon into 12 congruent parts
Hello, marspatrol!

Quote:

Draw 6 regular hexagons.
Then dissect each hexagon into twelve identical or congruent parts in 6 different ways.

A regular hexagon can be dissected into 24 equilateral triangles.

Code:

```          *---*---*         / \ / \ / \         *---*---*---*       / \ / \ / \ / \       *---*---*---*---*       \ / \ / \ / \ /         *---*---*---*         \ / \ / \ /           *---*---*```
Then the 12 congruent parts are diamond-shaped.
Code:

```        *       / \       *  *       \ /         *```

Here are two possible dissections . . .

Code:

```          *---*---*         / \  \  \         *  *---*---*       / \ / \  \  \       *  *  *---*---*       \ / \ /  /  /         *  *---*---*         \ /  /  /           *---*---*```

Code:

```          *---*---*         /  / \  \         *---*  *---*       / \  \ /  / \       *  *---*---*  *       \ /  / \  \ /         *---*  *---*         \  \ /  /           *---*---*```