Hummingbird or Periwinkle Quilt
 

I inherited 109 pieces like the picture shown and don't have a pattern or instructions for the background. I understand how to do the entire block from scratch but not from these already completed pieces. Any help would be appreciated!!

You could set it all together with diamond shapes, or you could just turn it into a square with long squat triangles. Depending on your skill set you could applique the blocks down instead of inserting the triangles.

You could also just say heck with the points and trim it slightly to make it an arc, like in a Double Wedding Ring design.

From what I've seen on pinterest you would join with an octogon.

https://www.google.com/search?q=Humm...QH3C7HfZdWPAM:

Here is another way, applique

https://susies-scraps.com/2018/08/19...ock-made-easy/

I assume that your photo has been taken from an angle and all 4 of the "kites" that make up this fractional block are the same size?

If so

If you have a 45 degree kaleidoscope wedge ruler (several of them on the market), I believe you could cut 8 triangles of appropriate sizes to make the corner triangles. I believe you'd want them to each be the width of a side of the periwinkle plus a half inch, but don't quote me. Measure one of the periwinkle sides including seams and then experiment with a strip of fabric until you figure out what the width of the strip should be to create a 45 degree kaliedescope wedge with a "short side" of the same length of the periwinkle blade length.

Sew one side of two of the kaleidoscope wedge triangles together long sides together This will create a "corner piece" that you can then seam to one corner of the periwinkle. You'll need 4 of these per block. I hope that makes sense.

If you do it right, you could probably avoid sewing corner seams by sewing the short end of two of the kaleidoscope triangles to the periwinkle and then seam them together.

I would use light interfacing to back and turn under the edges, then machine applique to background squares. The interfacing might help if some pieces are too fragile.

"Inherited". I inherited a big stack of little 9 patches. I think I know what the intent was but I wasn't into that and found a simpler way to put them into something meaningful to me. Now that finished quilt is on the bed and I'm enjoying it more than I did the box of 9 patches. Unless the one who made those blocks you have is around to see how they ended up--my method would be to cut those down into 4 patch blocks and find a way to use those in a project of your choosing. Finished is a great way to enjoy them!