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I'm sure I've learned a half dozen ways of making half square triangle units, but my favorite method is taking a square of background fabric and a square of fashion fabric, drawing a diagonal line on one square, sewing 1/4" away on either side of the line, and then cutting the two units apart on the drawn line. If the squares are oversized to begin with, you can square each unit up and have a perfect half-square triangle unit.
Last week I needed 560 half square triangle units, and I used a different method to make them, which is much faster and more efficient for multiple units in the same two fabrics. Maybe someone else will find it useful. I learned this method from a
Quilt University class I took a long time ago. I think this is the only time I've used it since that class, but it's one more skill you can add to your toolbox when the occasion arises. Before you start, you need to know what the unfinished dimension of your half square triangle unit is. Mine was 2-1/2" unfinished.
I cut two panels of fabric, one in the background fabric and one in the fashion fabric, 13" x the width of the fabric (40" or 42"). The height of the panel is determined by how many rows you want to cut out of that dimension. Since my units were 2-1/2", 5 rows of triangle units equal 12-1/2", and I allowed a little extra to square up the edges, so each of my panels was 13" high. You can certainly cut the panel taller if you want to, but a larger panel might be a little unwieldy to handle. In fact, you can manipulate the dimensions of these panels any way you want to, depending on how many units you need and what size you want them to be.
Next I layered the fabrics, right sides of both fabrics facing up, matching the lower edges of the fabrics. Then I squared up the left edge of the fabrics.
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Using the 45 degree line on my ruler, I cut bias strips all the way down the length of the panels. At this point you'll need to determine how wide to cut the strips.
Here's the formula:
finished size of unit x .71, rounded up to nearest 1/8", plus 1"
The finished size of my units will be 2", so 2 x .71 = 1.42
Round up to nearest 1/8" = 1-1/2"
Plus 1" = 2-1/2"
So I should cut my bias strips 2-1/2" wide.
The width of the strips determines how much waste you'll have between the half square triangle units. At 2-1/2" wide I had more waste than was desirable for me, so I reduced the width of my strips to 2-3/8", and that worked fine.
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Next, I sewed the panels back together, alternating a background strip with a fashion fabric strip. You'll have two panels like this after you've done all the sewing. Adding the seam allowances shrinks the panel across the width of the panel (the 40" dimension). It also shrinks the height (13") of the panel, but only in the corners where you didn't cut a strip across the full heighth of the panel.
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Placing the 45 degree mark on my ruler along one of the seam lines, I squared up one long edge of my panel.
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Next I cut rows, 2-1/2" wide, across the heighth of the panel, which is the dimension of the unfinished half square triangle unit I wanted. From my panel, I cut five rows, with a small amount of waste at the top of the panel.
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From each row, I cut half square triangle units. Because there is a small amount of waste between triangles, you'll need to flip each unit around and square it up.
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There will be some waste at the beginning and end of each row; and if I have enough fabric, I'll pair up these waste pieces and make a few additional half square triangle units.
From one set of panels, 13" x 40", I made 114 half square triangle units.