Area of a Square

In area of a square we will learn how to find the area by counting squares.

To find the area of a region of a closed plane figure, we draw the figure on a centimeter squared paper and then count the number of squares enclosed by the figure.

We know, that square is a rectangle whose length and breadth are equal. In a square all four sides are equal.

Therefore, area of a square = (side × side) square units = (side)2 square units.

In a square the length is equal to breadth.

Hence, area of a square = side × side

The number of 1 cm squares enclosed = 4

Area = 4 sq cm

4 = 2 × 2

Hence, area = side × side

The unit of sides and the corresponding units of areas as given below:

 Unit of Side Unit of Area mm square mm (sq mm) or mm2 cm square cm (sq cm) or cm2 m square m (sq m) or m2 km square km (sq km) or km2

Note: Write finding the area of a given figure, make sure that the sides (length or breadth) are in the same unit of length. If they are given in different units, change them to the same unit.

Look at the above figure. You can see that the area of a square having sides 2 cm each is equal to the area of 4 squares of sides 1 cm each = 4 cm2. It can also be expressed as 2 cm × 2 cm = 4 cm2. Area of a square is 2 times of its each side.

Solved examples to find the area of a square when side is given:

1. Find the area of a square of side 8 cm.

Area of a square = length (l) × length (l)

= 8 × 8 sq. cm.

= 64 sq. cm.

2. Find the area of a square of side 11 m.

Area of a square = length × length

= 11 × 11 sq. m.

= 121 sq. m.

3. Find the area of a square of side 49 cm.

Area of a square = length × length

= 49 × 49 sq. cm.

= 2401 sq. cm.

4. Find the area of a square of side 50 m.

Area of a square = length × length

= 50 × 50 sq. m.

= 2500 sq. m.

5. Find the area of a square photo frame whose side is 20 cm.

Area of the photo frame = 20 cm × 20 cm

= 400 sq. cm

6. Find the area of a square with side 9 cm.

Solution:

Area of the square = side x side

= 9 × 9 sq. cm

= 81 sq. cm

Worksheet on Area of a Square:

1. Find the area of the squares with the given side.

(i) 4 cm

(ii) 2.5 cm

(iii) 8 m

(iv) 90 mm

(v) 13.4 km

(i) 16 sq. cm

(ii) 6.25 sq. cm

(iii) 64 sq. m

(iv) 8100 sq. m

(v) 179.56 sq. km

2. Find the area of the squares whose side is:

(i) 4 cm

(ii) 20 cm

(iii) 6 m

(iv) 200 m

(v) 12 cm

(vi) 40 cm

(i) 16 sq. cm

(ii) 2500 sq. cm

(iii) 36 sq. m

(iv) 40000 sq. m

(v) 144 sq. cm

(vi) 1600 sq. cm

Word Problems on Area of a Square:

3. The area of a badminton court is 140 square m. If the breadth of the court is 7 m, then find its length.

20 m

4. The display board of class VII A is in the shape of a square. If the length of its side is 60 cm, then find its area.

3600 sq. cm

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