# 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 (s^{2}).

**Area of Square = side ^{2}**

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

If diagonal = d; then: s^{2 }+ s^{2} = d^{2}

⇒ 2s^{2 } = d^{2}

⇒ A = s^{2} = d^{2} /2

**Area of Square = (diagonal ^{2})/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 cm^{2}

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

**Solution:** Side of the square = s = 16 cm.

Area of the square = s^{2}

= 16^{2} cm^{2}

= 256 cm^{2}

**Question 3:** Find the length of the square whose area is 529 cm^{2}.

**Solution: **Area of the square = A = 529 cm^{2}

Side of the square = s = ?

Area of the square = A = s^{2}

⇒ 529 cm^{2 }= s^{2 }

⇒ 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 = d^{2}/2

= 16^{2}/2cm^{2}

= 256/2 cm^{2}

= 128 cm^{2}

**Question 5:** Find the length of the diagonal of a square whose area is 32 cm^{2}.

**Solution:** Area of the square = A = 32 cm^{2}**
**Diagonal of the square = d = ?

Area of the square = A = d

^{2}/2

⇒ 32 cm

^{2 }= d

^{2}/2

⇒ d = √64 cm

⇒ d = 8 cm

Hence the length of the diagonal of this square is 8 cm.

For area of a circle click here!

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