The characteristics of a square are that it is a regular quadrilateral with equal sides and four 90-degree angles. Quadrilaterals can only be squares if they match a list of conditions, including that they must have two adjacent equal sides and be a rhombus with all equal angles.
The perimeter of a square will have the length of four times the side length. The diagonals of the square will be of equal length.
When circles are inscribed around or inside of a square, the area of the circle is either pi / 2 if the circle is around the square or pi / 4 if the circle is inscribed inside of the square.