# Area of Square

Area of a square is the number of unit squares needed to fill in a square. It is simply defined as the area or the space occupied by it. Since the area of a square is the product of its two sides, the measurement is done in square units such as m2, cm2, and mm2.

## Formulas

### Using Side Length

The basic formula to calculate the area of a square is given below:

Let us solve few examples to understand the concept better.

Find the area of a square chamber of side 20 m.

Solution:

As we know,
Area (A) = a2, here a = 20 m
= (20 × 20) m2
= 400 m2

Find the area of a square-shaped swimming pool with side 33 feet.

Solution:

As we know,
Area (A) = a2, here a = 33 ft
= (33 × 33) ft2
= 1089 ft2

### Using Diagonal

The formula to calculate the area of a square when only diagonal is known is given below:

Derivation

In square ABCD,

Applying Pythagoras theorem, we get

d2 = a2 + a2

=> d2 = 2a2

=> d = a × √2

=> a = d/√2

Squaring both sides, we get

=> a2 = d2/2

Since, a2 = area (A) of square, the above equation can be written as

Area (A) = d2/2

Let us solve an example to understand the concept better.

Find the area of a square with a diagonal of 16 cm.

Solution:

Here, we will use an alternative formula to calculate the area of a square
Area (A) = d2/2, here d = 16 cm
= (16)2/2 cm2
= 128 cm2

### Using Perimeter

The formula to calculate the area of a square when only the perimeter is known is given below:

Derivation

As we know,

Perimeter (P) = 4 × side = 4a

=> a = P/4

Now, as we know

Area (A) = a2

Area (A) = (P/4)2

Let us solve a few examples to understand the concept better.

Find the area of a square park with a perimeter of 200 cm.

Solution:

As we know,
Area (A) = (P/4)2, here P = 200
= (200/4)2 cm2
= (50 × 50) cm2
= 2500 cm2
Alternative Method
As we know,
Perimeter (P) = 4 × side, here P = 200
=> 200 = 4 × side
=> side = 200/4 = 50 cm
Now, as we know
Area (A) = a2, here a = 50 cm
= (50 × 50) cm2
= 2500 cm2
Thus, the area of the square park of perimeter 200 cm is 2500 cm2

Find the cost of cementing a square floor of side 15 m if the rate of cementing is $10 per m². Solution: As we know, Area (A) = a2, here a = 15 m = (15 × 15) m2 = 225 m2 Now, since the rate of cementing is$10 per m²
Total cost of cementing the square floor = $(225 × 10) =$2250