GRE Geometry - Squares

A square is a special kind of rectangle, in that all of the sides are equal in length, not just opposite sides. The area of a square is base times height, but because all sides are equal, we usually say that the area of a square is length of a side squared. The perimeter of a square is four times the length of one of the sides. Example squares, with their area and perimeter indicated:

Notice that a square can be designated in one of several ways. All sides can be labeled, the sides can be given variables, such as x and y, the shape can be indicated to be a square, etc. As long as you know that a shape is a square, all that you need to know is the length of one side, after which it is then easy to determine the area and perimeter.

A few of the trickier GRE math problems will require you to calculate or use diagonals. A diagonal is just what it sounds, it diagonally connects two opposite corners of a square (a rectangle can have a diagonal, too). In the case of a square, we use the Pythagorean Theorem to derive the relationship between a side of a square and the diagonal of a square.