Exercise 1

Calculate the area and perimeter of a rectangle with a base of 10 cm and a height of 6 cm.

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Exercise 2

Calculate the number of trees that can be planted in a rectangular field which is 32 m long and 30 m wide if each tree needs 4 m² to grow.

Exercise 3

Calculate the number of square tiles needed to cover a rectangular surface of 4 m by 3 m if the length of each side of the tiles is 10 cm.

Exercise 4

A rectangular garden has dimensions of 30 m by 20 m and is divided in to 4 parts by two pathways that run perpendicular from its sides. One pathway has a width of 8 dm and the other, 7 dm. Calculate the total usable area of the garden.

Exercise 5

Calculate the length of the diagonal of a rectangle with a base of 10 cm and a height of 6 cm.

Exercise 6

A rectangular field has a length of 170 m and a width of 28 m. Calculate:

1 The area of the field in hectares.

2 The price to re-seed the field if each square meter costs $15.

Exercise 7

The length of the rectangle is 5 less than two times its width. The perimeter of the rectangle is 30 cm. Find the length and width of the rectangle.

Exercise 8

Calculate the length of the diagonal of a rectangle with a base of 10 cm and a height of 6 cm.

Exercise 9

A rectangular kitchen is 4 times as long as it is wide. the perimeter of the kitchen in 120 feet. What is its length and width?

Exercise 10

A rectangular pool is 300 cm long and 150 cm wide. How many square tiles of 15 cm length can fit into the pool?

Solution of exercise 1

Calculate the area and perimeter of a rectangle with a base of 10 cm and a height of 6 cm.

Exercise 1

Perimeter = 2 \cdot (10 + 6) = 32 cm

Area = 10 \cdot 6 = 60 cm^2

 

Solution of exercise 2

Calculate the number of trees that can be planted in a rectangular field which is 32 m long and 30 m wide if each tree needs 4 m² to grow.

Area = 32 \cdot 30 = 960 m^2

Trees that can be planted = \frac{960}{4} = 240

 

Solution of exercise 3

Calculate the number of square tiles needed to cover a rectangular surface of 4 m by 3 m if the length of each side of the tiles is 10 cm.

A _{S} = 4 \cdot 3 = 12 m^2 = 120000 cm^2

A_{B} = 10 \cdot 10 = 100 cm^2

= \frac{120000}{100} = 1200 tiles

 

Solution of exercise 4

A rectangular garden has dimensions of 30 m by 20 m and is divided in to 4 parts by two pathways that run perpendicular from its sides. One pathway has a width of 8 dm and the other, 7 dm. Calculate the total usable area of the garden.

 

Exercise 4

8 dm = 0.8 m

h = 20 - 0.8 = 19.2 m

7 dm = 0.7 m

b = 30 - 0.7 = 29.3m

A_{J} = 19.2 \cdot 29.3 = 562.56 m^2

 

Solution of exercise 5

Calculate the length of the diagonal of a rectangle with a base of 10 cm and a height of 6 cm.

Exercise 5

d^2 = 10^2 + 6^2

d = \sqrt{136} = 11.66 cm

 

Solution of exercise 6

A rectangular field has a length of 170 m and a width of 28 m. Calculate:

1 The area of the field in hectares.

2 The price to re-seed the field if each square meter costs $15.

Area of field in hectares

A = 170 \cdot 28 = 4760 m^2

\frac{4760}{10000} = 0.476 ha

Price to re-seed the field 

4760 \cdot 15 = $71400

Solution of Exercise 7

Suppose, the width of the rectangle = w = x

Length = l = 2x - 5

Perimeter of a rectangle = 2 (l + w) = 2l + 2w

50 = 2(2x - 5) + 2(x)

50 = 4x - 10 + 2x

50 = 6x - 10

50 + 10 = 6x

60 = 6x

x = 10

Width = 10 cm

Length = 2x - 5

              = 2 (10) - 5

              = 20 - 5

              = 15 cm

 

Solution of Exercise 8

The perimeter of the rectangle is 30 cm and its length is 10 cm. Calculate the length of the diagional of the rectangle.

To calculate the length of the diagonal, you must know the width of the rectangle.

Perimeter = 2l + 2w

30 = 2 (10) + 2w

10 = 2w

w = 5 cm

Length of the diagonal = d

d^2 = 10^2 + 5^2

d^2 = 125

d = \sqrt{125} cm

 

Solution of Exercise 9

l = 4w

Perimeter = 2l + 2w

Substitute l = 4w in the above equation:

Perimeter = 2 (4w) + 2w

120 = 8w + 2w

120 = 10 w

w = 12 feet

l = 4w

l = 4(12)

= 48 feet

Solution of Exercise 10

Length of the pool = l = 300 cm

Width of the pool = w = 150 cm

Length of the square tile = 15 cm

Square tiles that can fit along the length of the pool = \frac{300}{15} = 20

Square tiles that can fit along the width of the pool = \frac{150}{15} = 10

Total tiles that can fit into the pool = 20 x 10 = 200 tiles

 

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.