Formulary: Maths - Geometry - Square □

Square □

A square is a basic shape which has four equal sides and four equal right angles (90°).

Definitions:

  • a: Edge Length
  • d: Diagonal
  • U: Perimeter
  • A: Area
a a U d U

Perimeter of a Square

The perimeter U is the length of all 4 sides.

\( {\color{blue} {U}} = 4 \times {\color{red} {a} } \)
U = Perimeter
a = Edge Length

\( {\color{blue} {U}} =2 \times \sqrt{2} \times {\color{red} {d} } \)
U = Perimeter
d = Diagonal


a A d A

Area of a Square

The region inside a square.

\( {\color{OliveGreen} {A}} = {\color{red} {a} } \times {\color{red} {a} } = {\color{red} {a} }^{2} \)
A = Area
a = Edge Length

\( {\color{OliveGreen} {A}} = \frac{ {\color{red} {d} }^{2} }{2} \)
A = Area
d = Diagonal


a d

Pythagorean Theorem

\( d=sqrt(2*a^2) \)
d = Diagonal
a = Edge Length

\( a=sqrt( d^2/2 ) \)
a = Edge Length
d = Diagonal