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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.

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.

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.

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 $$2$$.