**Area of a Square**

Let us
find the formula to calculate the area of a square using the area of a
rectangle.

Consider a rectangle of length 5 cm
and breadth 3 cm. Draw this rectangle on a square grid sheet.

Count the number of squares that the rectangle covers. There are 15 squares. So, the area of a rectangle of sides 5 cm and 3 cm is 15 sq. cm.

Since 15 = 5 × 3, therefore the
product of the length and the breadth of the rectangle is equal to its area.

From this verified result, we can
conclude that

Area of a
rectangle = length × breadth

Let us consider the square now.

We know that a square is a rectangle
with all four sides equal.

We can use the same formula to find
the formula of area of a square.

Since, in a square, length = breadth

Area of a square = length × breadth =
length × length = side × side

**Area of
a square **= **(side) ^{2}**

**Area of a Square Formula**

**Area of a square**=

**(side)**

^{2}

^{}

**Area of a Square Example**

**Area of a Square Example**

**Example 1:** Find the area of a square whose each side measures 15 cm.

**Solution:** Given: side of the square = 15 cm

Area of a square = (side)^{2}

= (15)^{2}

= 225 sq. cm

**Example 2:** The area of a square is 576 sq. cm. Find the measure of each side
of the square.

**Solution:** Given: area of the square = 576 sq. cm

We know that,

Area of a square = (side)^{2}

576 = (side)^{2}

(side)^{2} = 24 ×
24

side
= 24

Hence, the measure of each side of
square is 24 cm.

**Example 3: **Find
the cost of levelling a square field of side 25 m at the rate of Rs 20 per sq.
m.

**Solution:**
Given: The length of each side of the field = 25 m

The area of the square field = side ×
side

= 25 × 25 = 625 sq. m

The cost of levelling the field = 625 ×
20

= Rs 12,500

**Example 4: **Ritu
runs 1 km to complete one round of a square park. Find the area of

the park. Also, find the cost of
levelling the park at Rs 8 per sq. m.

**Solution: **Given:
The side of the square park = 1000/4 m = 250 m

The area of the park = (side)^{2} =
(250)^{2} = 62,500
m^{2}

Cost of levelling the park = Rs 8
× 62,500 = Rs 5,00,000

Thus, the cost of levelling the park
at Rs 8 per sq. m is Rs 5,00,000.