Table of Contents

Last modified on August 3rd, 2023

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 m^{2}, cm^{2}, and mm^{2}.

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) = a^{2}, here a = 20 m

= (20 × 20) m^{2}

= 400 m^{2}

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

Solution:

As we know,

Area (A) = a^{2}, here a = 33 ft

= (33 × 33) ft^{2}

= 1089 ft^{2}

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

d^{2} = a^{2} + a^{2}

=> d^{2} = 2a^{2}

=> d = a × √2

=> a = d/√2

Squaring both sides, we get

=> a^{2} = d^{2}/2

Since, a^{2} = area (A) of square, the above equation can be written as

**Area ( A) = d^{2}/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) = d^{2}/2, here d = 16 cm

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

= 128 cm^{2}

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) = a^{2}

**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} cm^{2}

= (50 × 50) cm^{2}

= 2500 cm^{2}**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) = a^{2}, here a = 50 cm

= (50 × 50) cm^{2}

= 2500 cm^{2}

Thus, the area of the square park of perimeter 200 cm is 2500 cm^{2}

**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) = a^{2}, here a = 15 m

= (15 × 15) m^{2}

= 225 m^{2}

Now, since the rate of cementing is $10 per m²

Total cost of cementing the square floor = $ (225 × 10)

= $2250

Last modified on August 3rd, 2023