1. Properties of Geometric Shapes
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2. Square A 4-sided regular polygon with all sides equal and all internal angles 90°
Properties:
All four sides are congruent (same length)
Opposite sides are parallel
A square has two diagonals
the point where the diagonals intersect (cross), divides each diagonal into two equal parts
The diagonals are congruent. Each diagonal bisects the other. In other words each diagonal divides the square into two congruent isosceles right triangles. Because the triangles are congruent, they have the same area, and each triangle has half the area of the square.

3. Attributes
Vertex
The vertex 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.
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
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 s√2
where s is the length of any one side.