Originally Posted by the casual quilter
You could add a top and bottom border that is pieced or appliqued and then use your border fabric around all four sides. The mood of the colors or the pattern in the fabric in the carpenters square might tell you what piecing or applique would look good.
I agree. Add an inner border on top and bottom to complement the square, then add the outer border all around to pull it together. I feel like I have seen this often, but can't come up with an example when I need one!