A square is a fundamental shape in geometry, recognized for its perfect symmetry and equal sides. It is a special type of rectangle where all four sides are equal, and each angle measures \(90 ^\Circ\). Squares are widely used in mathematics, design, and architecture due to their uniform structure.
The perimeter is the total length around the square:
\[ P = 4 \times a \]
Where:
The area is the amount of space enclosed by the square:
\[ A = a^2 \]
The diagonal of a square is the line segment connecting two opposite corners:
\[ d = a \times \sqrt{2} \]
This formula comes from the Pythagorean theorem.