What about this? Attach the large triangle to the long side of the square/triangle set. Then add some additional 6" squares and get a block that looks like this, with the purple (or red in my pic) highlights. You will likely have to trim the large triangles, and the squares will be less than 6". Or I got a lovely hexagon block by adding more of the scrappy triangles instead of squares.
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If you like it an want actual measurements, let me know and I'll draw it up in EQ when I get home.