Squares and Rectangles

This example demonstrates the piecing of a 4", finished size, four square block section.

Calculate the width of the strips to cut. 2" finished square size + 1/2" seam allowance = 2 1/2" cut strip. Cut one strip of this width from each of the fabrics.
Sew these two strips together using a 1/4" seam allowance and press the seam allowance to one side. The strips should be 4 1/2" wide.
Square the end of the sewn strip being sure to remove the selvedge from the fabrics. Now, cut the strip into pieces 2 1/2" by 4 1/2".
Take two of the cut pieces and turn one of the pieces over so the different fabrics are opposite each other. You can check this by ensuring that the seam allowances go in opposite directions, this will then allow the pieces to nest together at the seam. Sew the pieces together using a 1/4" seam allowance and press the seam to one side. The finished block should measure 4 1/2".

To create blocks or block sections containing rectangles, calculate the finished length of the rectangle plus 1/2" for seam allowances and cut the pieced strip into pieces of this measurement.

Right Triangles

Right triangles, also called half square triangles, are composed of a square cut in half on the diagonal. Many quilt block patterns call for two right triangles to be joined together to form a square.

Calculate the finished size of the pieced square. Add 7/8" to that measurement for seam allowances. For example, 4" finished sized + 7/8" = 4 7/8" width of strip to cut.
Cut one fabric strip this width from each fabric.
Square one end of each fabric strip being sure to remove the fabric selvedge. Now, on the back of the lighter fabric strip, draw a line the same distance as the width of the strip from the squared strip end. In the example this would be 4 7/8". This should create a perfect square. Continue drawing lines 4 7/8" apart down the fabric strip until the required number of squares have been drawn.

Note: Each square will result in TWO pieced squares, so if the pattern calls for four right triangles in each color to be pieced together, draw two squares on the fabric strip.
Draw a line dividing each square in half on the diagonal. Extra Tip - if you draw the dividing line so that they are in opposite directions on each square you will be able to easily sew down the strip without cutting off your threads (a bit like chain stitching your patches together its just all one large patch).
Carefully place the lighter colored strip on top of the darker colored strip with the right sides of the fabric together and the edges in alignment. Sew 1/4" away from each of the diagonal lines.
Cut the strip apart on each of the vertical marked lines to create the squares, then cut each square on the diagonally marked lines to create two triangles. Open up the triangle shaped piece, press seam to darker fabric.

Quarter Triangles

Another common piece used in quilt block construction is the quarter triangle (or sometimes known as the quarter square triangle. A quarter triangle is formed by a square cut in half twice on the diagonal. Many blocks use quarter triangles joined together to form right triangles in their construction. The steps to piece quarter triangles is very similar to those of piecing right triangles except for the following variations.

The initial strips must be cut the finished square size plus 1 1/4" for seam allowances instead of 7/8". For a square composed of quarter triangles to have a finished size of 4", the initial strips must be cut 4" finished size + 1 1/4" seam allowances = 5 1/4" wide.
After cutting the sewn strips apart on the marked lines, each unit must be cut in half again from the corner, to the middle of the longest side. Open up the triangle shaped piece, press seam to darker fabric and then with two of these right sides facing sew the long edges together, again using a 1/4" seam allowance, also ensuring the two seams nest together for that perfect join. (Don't forget to match the opposite fabrics together).
Each marked square will result in four pieced quarter triangle units.