Area of a Square

Area of a Square

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

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 m2

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.

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