### 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.
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 length of each side of a square.
(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 $$2$$.