Theory:

Area of a square: The area of the square is the product (multiply) of the length of its sides.
 
area1.png

Area \(=\) side \(×\) side.
 
Area (\(A\)) \(= a × a = a²\) square units or \(A = a²\) or \(a² = A\) or \(a = √A\).
 
Where '\(a\)' denotes the side of the square.

Side of the square \(= P/4\) units.
 
Given the diagonals(\(d\)), the area of a square \(= 1/2×(d²)\) \(=\) \(d²/2\).
The perimeter of a square: The perimeter of a square is the sum of the length of its sides.
 
perimater.png

The perimeter(\(p\)) \(=\) \(AB + BC + CD + DA\) or \(p =\) \((a + a + a + a)\) \(= 4a\) units.

Where '\(a\)' denotes the length of each side of a square.
Diagonals of a square: Diagonals of a square are equal in length, they bisect the angles, and they are the perpendicular bisectors of each other.
 
diagonal.png

Length of the diagonal
(\(d\)) \(=\ √(a² + a²)\ = √(2a²)\ = a√2\) units.

Where '\(d\)' denotes a diagonal of a square is equal to side length times square root of \(2\).