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.

$Square$

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.

$Area of a Square$

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

Questions and Answers 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

Answers:

(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

Answers:

(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.

Answer:

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.

Answer:

3600 sq. cm

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