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?