what are the possible ways to divide a square as 4 equal parts
It sounds like a homework. In reality yes, it has something to do with graphic design.
It is the kind of analisis of shapes and transformations that one make in the first semesters of a carreer.
You really need to imagine things, see things, and feel the answer.
A) It is enough if you simply modify some center lines in equal relationship to each sub-square, and rotate that segment 90°.
B) If you think of a square as part of a multi dimensional square pattern universe :o), you can invade each square with a twin square. You have two separated shapes, but together they are simply a split shape, but all 4 splited shapes are equal, so it is valid.
C) And if you think outside the box, I mean, the square, you can join this pices, move them an assemble them. Combine this with the first case and you achive interesting patterns.
This is the kind of thinking that you need to develop. But I am worried if you are studying design. You need to explore, not simply ask someone else.