AREA OF RECTANGLE WORD PROBLEMS WORKSHEET

Problem 1 :

A rectangular paddock is 800 m by 1.5 km. 

a) Find the area of the paddock in hectares.

b) If fertilizer costs $50 per hectare, how much will it cost to fertilize the paddock?

Problem 2 :

A corn field is 2 km by 3.2 km.

Find : 

a) the area of the property in hectares

b) the total cost of sowing a crop if it costs $80 per hectare.

Problem 3 :

A football pitch is 50 m by 90 m.

a) Find the area of the pitch.

b) How long will it take to mow the whole pitch if 60 square meters can be mown each minute?

Problem 4 :

Floor tiles are 20 cm by 30 cm.

a) How many tiles would you need to tile a floor 5 m by 6 m?

b) If each tile costs $6.85, find the total cost of the tiles.

Problem 5 :

A driveway is 23 m long and 3 m wide. Find the total cost of concreting the driveway if the materials cost $20 per square meter and the cost of hiring labor to do the concreting is $25 per square meter.

Problem 6 :

What would be the cost of resurfacing a 50 m by 32 m gymnasium floor with a rubberized compound costing $35.60 a square meter?

Problem 7 :

A farmer has a field that is 300 m long and 70m wide. Calculate the area of the field.

Problem 8 :

A piece of paper has a length of 18 cm and a width of 6cm. Find the area of paper.

Problem 9 :

A rectangular carpet has an area of 20 sq m. If the length is twice the breadth, what is the breadth?

Problem 10 :

If the perimeter of a rectangle is 100 cm and its width is 32 m, then find the length of the rectangle.

1. Solution :

(a)  Length of paddock  =  800 m and width  =  1.5 km

1000 m  =  1 km

1.5 km  =  1.5(1000)

=  1500 m

Area of paddock  =  length x width

=  800(1500)

=  1200000 m²

10000 m²  =  1 hectare

=  120 hectare

(b)  Cost of fertilizer  =  $50 per hectare

Required cost  =  120(50)

=  6000

So, the required cost to fertilize the paddock is $6000.

2. Solution :

Length of corn field  =  2 km and width  =  3.2 km

(a)  Area of the property  =  length x width

=  2 x 3.2

=  6.4 km²

1 km²  =  100 hectare

=  6.4 (100)

=  640 hectare

(b)  Cost of sowing crop  =  $80 per hectare

=  80(640)

=  $51200

3. Solution :

(a)  Length of pitch  =  50 m and width  =  90 m

Area of pitch  =  50(90)

=  4500 m²

(b)  Number of square meters he can mow in one minute

=  60 m²

Time taken to mow 4500 m²  =  4500/60

=  75 minutes

75  =  1 hour + 15 minutes

So, time taken is 1 hour and 15 minutes.

4. Solution :

Length of 1 tile  =  20 cm and width  =  30 cm

Area of one square tile  =  30(20)

=  600 cm²

(a)  Area of floor  =  5(6)

length  =  500 cm and width  =  600 cm

=  300000 cm²

Number of tiles required to cover the floor

=  300000/600

=  500

So, the number of tiles required is 500.

(b)  Cost of one tile  =  $6.85

Required cost  =  500(6.85)

=  $3425

So, total cost of tiles is $3425.

5. Solution :

Length of drive way  =  23 m and width  =  3 m

Area of driveway  =  23(3)

=  69 m²

Materials cost  =  $20 per m²

Labor cost for concreting  =  $25 per m²

Material cost for drive way  =  69(20)

=  $1380

Labor cost for drive way  =  69(25)

=  $1725

Total cost  =  1380 + 1725

=  $3105

6. Solution :

Length  =  50 m and width  =  32 m

Area of gymnasium floor  =  50(32)

=  1600 m²

Compound costing per square meter  =  $35.60

Required cost  =  1600(35.60)

=  $56960

7. Solution :

Length of the field = 300 m

width = 70 m

Area of the field = length x width

= 300 x 70

= 2100 square meter

So, the required area of the field is 2100 square meter.

8. Solution :

Length of paper = 18 cm

width of paper = 6 cm

area of paper = 18 x 6

= 108 square cm.

Area of paper is 108 square cm.

9. Solution :

Let x be the breadth of the rectangle, then length be 2x.

Area of the rectangle = 20 sq.m

length x width = 20 sq.m

x(2x) = 20

2x² = 20

x² = 10

x = √10

So, the breadth of the rectangle is √10 cm

10. Solution :

Perimeter of rectangle = 100 cm

Width = 32 m

2(length + width) = 100

2(length + 32) = 100

length + 32 = 100/2

length + 32 = 50

length = 50 - 32

= 18 m

So, the required length of the rectangle is 18 m.

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