Square

 Side $$S$$ Diagonal $$d$$
$$2p = S \times 4$$
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

1. Four congruent sides
2. Four congruent right angles
3. Diagonals are perpendicular
4. 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 = S2
Side S = 2p / 4
Side S = √A
Diagonal d = S × √2
Side S = d / √2
Area A = d2 / 2
Diagonal d = √(2A)