### Theory:

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

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.

Side of the square \(= P/4\) units.

for, diagonals area of square \(= 1/2(d²)\)

**The perimeter of a square:**The perimeter of a square is the sum of the length of its sides.

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

Where \(a\) denotes the side of the square, the length of each side of a square is \(a\) units.

(

**Note:**The perimeter is equal to the sum of all sides).**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.

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

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