Like the triangles, there are a myriad of ways to create squares and rectangles. For the time being, I will refer to squares only. Rectangles are squares that have been stretched. Just keep going if you need a rectangle.
The basic way to create a square is to start at the bottom or side and move to the opposite end until you have a square. The hardest part is determining when a square has been reached. Do I stretch it or not? Do I finish the pattern repeat and make it slightly too long or work to the square and cut the pattern repeat off in perhaps an awkward place?
A fourth way to work this shape is going corner to corner. This has been popular in some of the crochet groups on Facebook for a while. Some have even come up with a way of making them graphgahns or putting a picture on while working from a corner to the opposite corner. This shape can be also adapted to rectangles. This can work with mitered squares as well as other modular types of knitting and crocheting.
Corner to corner (C2C) starting top
left or bottom right
Mitered Knit squares with Join as you go pick up
for all but the first block
A fifth way is to work in pieces. Choose the motif shape you want, triangle, square, rectangle, octagon, whatever shape you think will make a beautiful shawl. The shapes are then joined with either seams that are solid or openwork.
There is one other way to create a rectangle shawl. It's as a parallelogram. This has one end point going straight out at the top and the bottom of the rectangle goes up to meet the part that goes straight out. Then, on the other end, the bottom of the shawl goes out and the top corner of the rectangle goes down and out to meet the bottom line. This is an easy wear shape and adds a bit of interest for the creator as well as the wearer.
Something about square shawls to consider is how you will be wearing it. If you will be folding it, you will lose some of the definition of the lace. Square shawls can be difficult to wear without folding. Shawls can be a blessing while traveling however. They can double as blankets if your room is too cool and you can't control the thermostat. Shawls can be easy to stash in your purse or carry bag to pull out when you get cool even if no one else is feeling the temperature. They can also work to keep the sun off you.