Vertex The vertex (plural: vertices) is a corner of the square. Every square has four vertices.
Perimeter The distance around the square. All four sides are by definition the same length, so the perimeter is four times the length of one side, or:
perimeter = 4s
where s is the length of one side. See also Perimeter of a square.
Area Like most quadrilaterals, the area is the length of one side times the perpendicular height. So in a square this is simply:
area = s2
where s is the length of one side. See also Area of a square.
Diagonals Each diagonal of a square is the perpendicular bisector of the other. That is, each cuts the other into two equal parts, and they cross and right angles (90°).
The length of each diagonal is
where s is the length of any one side.