Exercise 1.2 (Area of the rectangle and square)

Exercise 1.2

1. The length of the side of each square is given below. Find its area.

(i) 10 metres

(ii) 5 cm

(iii) 15 metres

(iv) 16 cm

(i) 10 metres

Side = 10m

Area of the square = a­²

= 10²

=100sq.m

(ii) 5 cm

Side = 5cm

Area of the square = a­²

= 5²

= 25 sq.cm

(iii) 15 metres

Side = 15cm

Area of the square = a­²

= 15²

= 225sq.m

(iv) 16 cm

Side = 16cm

Area of the square = a­²

= 16²

=256sq.cm

2. Find the area of the following rectangles.

(i) length = 6 cm and breadth = 3 cm

Area = 1 × b

= 6×3

= 18 sq.cm

(ii) length = 7 m and breadth = 4 m

Area = 1 × b

= 7 × 4

= 28 sq.cm

(iii) length = 8 cm and breadth = 5 cm

Area = 1 × b

= 8×5

= 40 sq.cm

(iv) length = 9 m and breadth = 6 m

Area = 1 × b

= 9 × 6

= 54 sq.cm

3. If the cost of 1 sq.m of a plot is ₹ 800, then find the total cost of the plot that is 15 m long and 10 m breadth.

Length of the plot = 15m

Breadth of the plot = 10m

Area of the plot = 1 × b

= 15×10 =150sq.m

Cost of 1 sq.m = ₹ 800

Cost of 150 sq.m = 800 × 150 = 1,20,000

Answer : Cost of 150sq.m of a plot = ₹ 1,20,000

4. The side of a square is 6 cm. The length of a rectangle is 10 cm and its breadth is 4 cm. Find the perimeter and area of both the square and rectangle.

Step :1

Side of a square = 6cm

Area of a square = a²

= 6² = 36 sq.cm

Perimeter of a square = 4a

= 4 × 6 = 24cm

Step:2

length of a rectangle = 10cm

Breadth of a rectangle = 4cm

Area of a rectangle = 1 × b

= 10 × 4 = 40 sq.cm

Perimeter of rectangle = (2 ×1) + (2 × b)

= (2 × 10) + (2 × 4)

= 20 + 8 = 28cm

Answer:

Area of the square = 36 sq.cm

Perimeter of a square = 24cm

Area of a rectangle = 40sq.cm

Perimeter of a rectangle = 28cm

5. What will be the labour cost of laying the floor of an assembly hall which is 14 m long and 10 m breadth if the cost of laying is ₹ 60 per sq.m?

Length of the assembly hall = 14m

Breadth of an assembly hall = 10m

Area of a rectangle hall = 1 × b

= 14 × 10 = 140 sq.m

Cost of laying floor for 1sq.m = ₹ 60’

Cost of laying floor for 140 sq.m = 140 × 60 =8400

Answer: Cost of laying floor for 140 sq.m = ₹ 8400

Answer:

Exercise 1.2

1. (i) 100 sq.m (ii) 2.5 sq.m (iii) 40 sq.cm (iv) 54 sq.m

2. (i) 18 sq.cm (ii) 28 sq.m (iii) 40 sq.cm (iv) 54 sq.m

3. 1,20,000

4. 24cm; 36 sq.cm; 28cm; 140 sq.cm

5. 8,400

Activity 2

Using the grid sheet find the area and perimeter of the rectangles and squares. Each square is 1 sq. cm.

a) Area of square = a²

a² = 4

a = 2

Perimeter = 4a

= 4 × 2

= 8 units

b) Area of square = a²

a² = 9

a = 3

Perimeter = 4a

= 4 × 3

= 12 units

c) Area of square = 1 × b

= 5 × 2

= 10sq.cm

Perimeter = 2 ( 1+b)

= 2 (5 +2)

= 14 units

d) Area of rectangle = 1 × b

= 5 × 3

= 15sq.cm

Perimeter =2( l +b )

= 2 (5 +3)

=16 units