The math (eek!) is easy. Simply add 1.25 inches to the desired finished size square. For example, add 1.25 + 6 inches (finished square) = 7.25 inches. You would cut a square 7.25 inches and divide twice diagonally to yield four quarter square triangles. Quarter square triangles have straight of the grain on the outer (longest) side, with two bias edges. Half-square triangles, on the other hand, have two straight of grain sides and one bias. They are NOT interchangeable. Using these triangles correctly adds stability to your blocks and settings.
Easy enough. But what happens when you don't have enough fabric to cut a full square? What if you are working with scraps? I had a group of fabrics that I had cut all the squares I could but still lacked a bunch of triangles to finish the project in the size I wanted. So I took one of the quarter square triangles I had cut from a square and laid my ruler on it, matching the short sides to the edges of my ruler.
I placed some of the green painters tape on the wrong side of the ruler as shown here. Now I have an exact mark to cut quarter square triangles with. The tape acts as a bumper to place along the straight edge of the fabric.
Here is a scrap of fabric, the ruler aligned with the tape against the straight (cross or lengthwise) grain. I can cut the two straight sides for a perfect quarter square triangle in the size I need! If I had had more fabric or wanted a great many triangles of this fabric, I could have cut a strip the width of the triangle and alternated the template to cut with no waste.
The muslin triangle is cut from a square; the blue one from the scrap. Exactly the same size! And I was able to finish the project as planned.
Now, you're asking, what happens if you are cutting all scraps and don't even have enough for one full square in the right size? Simple! Cut a square of paper the correct size, divide it twice diagonally and carry on as shown above! Other than the addition of 1.25 inches to the finished size of the block, there is no other math with this method!
So there you have it--another tutorial. Simple but effective.