Here are some tips on 45°-90°
triangle measurements. These triangles are also known as half
squares or quarter squares, or short or long side measured
triangles, because of how they relate to squares.
The figures show the general relationships, and the table below gives specific measurements for ARDCOTM short or long side measured 45°-90° triangle products.
The figure at right shows how half squares are formed from a
square. As shown, the short sides of the triangle are the same as
the sides of the square that was cut in half. The long side of the
triangle, or hypotenuse, will generally be an unusual length
because of the 1.414 factor. Therefore it is usually easier to
refer to the length of the short side, and we call these "short
side measured." Also, the two smaller angles of the triangle are
half of the square's corner angle, or 45°, and the larger angle
is the same as the corner of the square, or 90° This explains
how the names "45°-90°" or "short side measured" or "half
square" can all refer to the same triangle.
The figure at left left shows how
quarter squares are formed from a square. As shown, the long side
of the triangle, or hypotenuse, is the same as the sides of the
square that was cut into quarters. In this case, the short sides of
the triangle will generally be an unusual length because of the
1.414 factor. Therefore it is usually easier to refer to the length
of the long side of the triangle, and we call these "long side
measured." Again, the two smaller angles of the triangle are half
of the square's corner angle, or 45°, and the larger angle is
the same as the corner of the square, or 90° This explains how
the names "45°-90°" or "long side measured " or "quarter
square" can all refer to the same triangle.
In fact, the basic shape and relationships of all these 45°-90° triangles is the same. The only difference is the size of square that is formed by putting together two or four of the triangles. If you put two together, then the short side will be the square size. If you put four together, then the long side will be the square size.
ARDCOTM product measurements are on the inside of the template, which is also the finished size of the piece. The quarter-inch seam allowance is added uniformly around the outside. In our part codes below, FTW refers to Forty-five degree Triangle Window template. The number part of the code is the length of the measured side. The measured side is the short side unless an H is appended, in which case it is the hypotenuse, or long side.