The piece of fabric you fold in half and sew along the inside border


Flange:
An inside decorative border element, or an outside border, in which a strip of fabric is folded wrong sides together, and sewn into the quilt, or as a decoration of a pillow. Think of a pillow sham, it is the outer fabric surrounding the sham. In a quilt, the flange is often inserted as a border in between the quilt top and an outer border, or between two borders. Think of piping but without the cord inside the piping that makes it stiffer.

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Adding A Flange
Measure the height of your quilt top.
Determine the width of your desired finished flange.
Multiply the width by 2, and add 1/2" for the seam allowances.
Cut your strip by that measurement, by the height.
Fold the strip in half, wrong sides together, and attach to your quilt top aligning the raw edges of the flange with the raw edges of the top, and the next outside border. Pin in place.
Sew on with a 1/4" seam allowance.
Repeat for the top and bottom borders.
For a cleaner appearance, attach the flange in between two borders, then attach the whole large border using a mitered seam.