# Area of a Square

## What is a square?

A square is a 2-dimensional (meaning flat) figure or shape, having four equal sides and each interior angle equal to 90°. It can be thought of as a rectangle with all sides equal. It has all general properties of a parallelogram.  this article is on area of a square. It is worth listing down all the properties of a square:

• Opposite sides are parallel.
• All sides are equal.
• All interior angles are 90°.
• Diagonals are of equal length and bisect each other at right angles.

A square fits the definition of a quadrilateral, a parallelogram, a rectangle and a rhombus.

## Area of a Square

Area is basically the quantity that expresses the measure of the extent of a 2-dimensional figure or shape. If the side of a square is given by ‘s’ then the formula of the area (A) is given by  (s2).

Area of Square = side2

We also know that the side and diagonal of a square are related through famous Pythagoras Theorem.

If diagonal = d; then:       s+ s2 = d2

⇒  2s =  d2

⇒  A =  s2  =  d2 /2

Area of Square = (diagonal2)/2

## Solved Examples

Question 1: Find the area of a square of side 5 cm.

Solution:

A square of side 5 cm would look like as shown aside. Formula for the area of a square is  (side)2.

Hence, Area of square = 5 cm x 5 cm  = 25 cm2

Question 2: Find the area of a square of side 16 cm.

Solution:

Side of the square = s = 16 cm.

Area of the square  = s2
= 162 cm2
= 256 cm2

Question 3: Find the length of the square whose area is 529 cm2.
Solution:
Area of the square = A = 529 cm2
Side of the square = s = ?
Area of the square = A = s2
⇒ 529 cm= s
⇒ s = 529 cm
⇒ s = 23 cm
Hence the length of the side of this square is 23 cm.
Question 4: Find the area of the square whose diagonal is  16 cm.

Solution:

Diagonal of the square = d = 16 cm.
Area of the square  = d2/2
= 162/2cm2
= 256/2 cm2
= 128 cm2
Question 5: Find the length of the diagonal of a square whose area is 32 cm2.
Solution:
Area of the square = A = 32 cm2
Diagonal of the square = d = ?
Area of the square = A = d2/2
⇒ 32 cm= d2/2
⇒ d = √64 cm
⇒ d = 8 cm
Hence the length of the diagonal of this square is 8 cm.