Building Polygons

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You have many squares and equilateral triangles all with the same side length. In this problem we want to build polygons by putting the squares and triangles as shown in the upper illustration. The illustration shows how we can build polygons with 3, 4, 5, or 6 sides.

But, you are not allowed to build polygons like the ones in the bottom illustration. If you could put an elastic band around those polygons, there would be empty spaces.

Can you build polygons with 7, 8, 9, 10, 11 and 12 sides like the ones in the upper illustration?

 
Posted: December 11, 2007
Puzzle
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Sword of Knowledge Counting the Triangles
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