

$$2p = S \times 4$$
Perimeter
$$S = \frac{2p}{4}$$
$$A = {S}^{2}$$
Area
$$S = \sqrt{A}$$
$$d = S \sqrt{2}$$
Diagonal
$$S = \frac{d}{\sqrt{2}}$$
$$A = \frac{{d}^{2}}{2}$$
Area
$$d = \sqrt{2A}$$
Definition
A square is a polygon with four sides and four congruent angles (right angles).
Properties
 Four congruent sides
 Four congruent right angles
 Diagonals are perpendicular
 The diagonal makes two right congruent triangles. In particular every triangle has angles of 45°, 45°, 90°
Square Formulas
Data  Formula 

Perimeter  2p = S × 4 
Area  A = S^{2} 
Side  S = 2p / 4 
Side  S = √A 
Diagonal  d = S × √2 
Side  S = d / √2 
Area  A = d^{2} / 2 
Diagonal  d = √(2A) 