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Making Squares in Squares

Using Half Square Triangles

In Lesson #5, you learned how to make a Square in a Square by adding small squares to the corners of a larger block. 

This lesson will show you have you can add continuous squares to a block by using Half Square Triangles.

Brace Yourself - There will be math!

Look at the picture on the top of the page.  There is one center square, and it is surrounded by four half square triangles.

The is another "round" of half square triangles after that, which you can see in the picture below.

We learned how to construct Half Square Triangles in Lesson #3.   You learned that you cut a square on the diagonal to make a half square triangle.

Your must use half square triangles so that the small sides will be on the grain.  As you can see from the picture  the small sides of the triangle, no matter how many rounds you add, will always be the outside edges of the block after each round.

What you are going to learn in this lesson is how to do the math so you know how big to cut the squares (that you are going to cut on the diagonal).

When you have a 45 degree triangle (with two equal sides, and one longer side, an isosceles triangle ),  you can figure out how long the hypotenuse will be if you know the measurement of one of the smaller sides.  The long side will be the measurement of the small side x 1.4142 inches.

If you know the measurement of the long side (hypotenuse), you can figure out the measurement of the smaller side by doing the opposite- dividing the measurement of the long side by 1.4142.

Since we want our triangle to fit the square,  we already know the measurement of the long side of the triangle.  So we just need to do the math to figure out the short side.

In addition:  We learned in the Triangle Lesson that when you join the pieces, you are going to have to add 3/8 inch for the seam allowance (raw)

So, in determining the square size, we just do the division, and then add the 3/8 inch to that.

Let's say we are starting with a 4-inch square.  We will divide 4 inches by 1.4142, which comes out to  2.82.  Now we add 3/8 inch (.375).  That comes out to 3.195.

You can round that off to the nearest 1/4 inch.  You may want to round up, since you are going to have to trim each round anyway.  So 3.195 becomes 3.2 or 3.25 which is 3 1/4 inches.

That is the size of the square you make, and then cut diagonally.  You need 4 squares, so you will have to do it twice.

Now for the trimming:  Once of the easiest ways to trim is with the Triangular shaped Easy Angle Ruler.











In this picture above, the long side of the Easy Angle  ruler is put on the edge of the fabric to be trimmed.  You want to leave 1/4 inch seam allowance (so as not to cut off the points).  You should be able to see that in the picture.

On the ruler you will have a couple diagonal lines that you can match up with the corner of your square.

Trim by making  straight cut right up the side of the block.

If you don't have the Easy Angle ruler, you can use any ruler and just line it up with the straight lines of the block, keeping the 1/4 inch seam allowance.


Here is another tip that will help you.  You sew the triangles on opposite sides first, and press.  It will be easier to sew on the last two triangles if you trim the first two triangles as show in the picture.  Just cut straight along the edge of the fabric.

Also, if you can't visually center the two pieces together, fold them in half and finger press them, or use an iron.  100% cotton has a memory, and just finger pressing them will usually leave enough of a mark.

   Another reason you want to center the blocks is so that the triangles are even.  If you look at the blue block, you can see how the points are suppose to line up.  See the horizontal line in the middle of the block?  The white color is the back of the triangles, which have been placed on the blue Batik fabric.  


The Snail's Tail Challenge Block has three rounds of squares.  If this lesson was a little hard to understand, see if this page will help.

The Square in a Square Block has lots of design possibilities.  If you practice this block, and learn the math, you have advanced to the next level!

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