Functional Skills Mathematics€¦ · ©West Nottinghamshire College. 2 . Excellence in skills...

Functional SkillsMathematics

Level 2

Learning Resource 12Perimeter and Area

MSS1/L2.7 MSS1/L2.8

PERIMETER AND AREA LEVEL 2

©West Nottinghamshire College 2

Excellence in skills development

12

Contents

Perimeter and Area Definitions MSS1/L2.7 Page 3 Circumference of a Circle MSS1/L2.7 Page 4 - 5 Area of a Parallelogram MSS1/L2.7 Page 6 Area of a Triangle MSS1/L2.7 Page 7 Area of a Trapezium MSS1/L2.7 Page 7 Area of a Circle MSS1/L2.7 Page 8 - 9 Perimeter and Area MSS1/L2.7 Page 10 Perimeter and Area Problems MSS1/L2.7 Page 11 Composite Shapes MSS1/L2.8 Page 12 - 13 Borders MSS1/L2.8 Page 14 - 16


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Excellence in skills development Learning Objective Perimeter and Area Definitions Learners should be taught to understand and use given formulae for finding perimeters and areas of regular shapes. Information The perimeter of a rectangle is the distance around the edge. The circumference of a circle is the distance around the edge. The diameter of a circle is the distance across the centre. The radius of a circle is the distance from the edge to the centre. You may use a calculator in this workbook.


PERIMETER AND AREA

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Excellence in skills development Information Circumference of a Circle The distance around the edge of a circle has a special name. It is called the circumference. The circumference is just like the perimeter but is only used when talking about circles. If you know the radius or the diameter of a circle, you can calculate its circumference. The circumference is given by:

C = 2 π r Where C is the circumference; r is the radius; π is a special number and is always 3.14 (to 2 d.p.).

Examples Example 1 Example 2

6 cm

The radius is half the length of the diameter.

r = 26

r = 3 cm

C = 2 π r C = 2 × 3.14 × 3 Circumference = 18.84 cm

Diameter = 6 cm Firstly we need to find the radius.

5 cm

Radius = 5 cm C = 2 π r C = 2 × 3.14 × 5

Circumference = 31.4 cm



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Excellence in skills development Exercise 1 Circumference of a Circle Find the circumference of each of the following circles: 1) 2)

5 cm 2 cm 3) 4)

12 cm 8 cm

5) 6)

16.4 cm

2.4 cm



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Excellence in skills development Information Area of a Parallelogram In a parallelogram the opposite sides are parallel.


Parallelogram area = b × h A = b × h

Height (h)

Base (b) Example 6 cm 8 cm Area = b × h = 8 × 6 = 48 Area = 48 cm2


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Excellence in skills development Information Area of a Triangle


Height (h) Triangle Area = Base × Height = b × h

2 2

Base (b) A = b × h

2

Area of a Trapezium (a)

Trapezium Area = (a + b) × Height (h) Height 2 (h)

Base (b) A = (a + b) × h 2


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Excellence in skills development Information Area of a Circle The area of a circle is given by:

Area = π × (radius) 2

A = π r 2 Example

5 cm

Area = π r 2 = π × 52 = 3.14 × 25 = 78.5 cm2 Remember that area always has square units. In this case, since the radius is in cm, the area is in square centimetres (cm2).



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Excellence in skills development Exercise 2 Area of a Circle Find the area of the following circles: 1) 2)

2 cm

4 cm

3) 4)

1.4 cm 8 cm

5) 6)

18 cm 3.4 cm



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Excellence in skills development Exercise 3 Perimeter and Area For each of the following shapes, find:

a) the perimeter or circumference

b) the area 1)


2.6 cm 4.3 cm 2) 5 cm

12 cm

13 cm 3) 6 cm 5 cm 5 cm 4 cm 10 cm 4)

8.2 cm


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Excellence in skills development Exercise 4 Perimeter and Area Problems 1) A circular pond has a diameter of 3.2 m.

a) What is the area of the pond?

b) What is the circumference? 2) A baseball stadium has a circular pitch with a radius of 100 metres.

a) The groundsman is going to use a fertilizer and needs to know the area of the pitch. What is the area?

b) He also needs to know what the distance is all the way round. What is this

dimension called and what is its value? 3) The diameter of the Earth at the equator is rather difficult to measure – we would need

to dig a very long tunnel!! It is much easier to measure the circumference. The circumference of the Earth is 40,000 km. Can you calculate its diameter? Hint: To find the radius, you will need to use the formula for the circumference of a circle.



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Excellence in skills development Learning Objective Composite Shapes Learners should be taught to understand and use given formulae for finding areas of composite shapes. Information The area of a composite shape is calculated by splitting the shape into separate shapes. The area of each one is then calculated and the areas are added together to find the total area. In the examples below, the shapes have been divided into two shapes. Examples Example 1 Example 2

5 cm

D

C


A

B

4 cm

6 cm

4 cm

7 cm 3 cm

4 cm Area of shape A = 6 × 4 = 24 cm2

B = 3 × 2 = 6 cm2 Total Area = 24 + 6 = 30 cm2

Area of shape C = 21

D = 4 × 3 = 12 cm2 Total Area = 10 + 12

= 22 cm2

(5 × 4) = 10 cm2


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Excellence in skills development Exercise 5 Composite Shapes 1) You need to order turf to make a new lawn as illustrated below:

12.4 m


7.8 m

8.6 m

4.6 m

Find the total area in order that you can buy the correct amount of square metres of turf.

2) A triangular shape has to be painted on some scenery in an outdoor theatre. The

triangle has a base of 6 m and a height of 7 m. To calculate the amount of paint required, find the total area.


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Excellence in skills development Information Borders

12 m

9 m

2 m border To calculate the area of the border:

(area of large rectangle) - (area of small rectangle) (12 x 9) - (8 x 5) 108 - 40 = 68 m2

You must make all units the same before you work out the area.



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Excellence in skills development Exercise 6 Borders 1) A photographer sells three sizes of photographs with borders.

For each size, find the area of: a) the photograph without its border; b) the photograph and border together; c) the border.

X

13.5 cm

16.5 cm 2 cm border Y

24.4 cm

19.85 cm

2 cm border

10.5 cm

13.5 cm

Z 1 cm border



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Excellence in skills development Exercise 6 cont Borders 2) A rectangular garden is 18.5 m long and 12.4 m wide. It has a central lawn

10.8 m long and 6.5 m wide. Find the area of:

a) the garden b) the lawn c) the border round the lawn

3) A postcard 14.2 cm by 9.5 cm has a stamp in one corner. The stamp is 24 mm by

2 cm. Find the area of:

a) the postcard b) the stamp c) the postcard not covered by the stamp.

4) A garden has a lawn 8.2 m long and 6·5 m wide. The border round the lawn is 1.5 m

wide on each side as shown. Find:

a) the area of the lawn b) the length l of the garden c) the width w of the garden d) the total area of the garden e) the area of the border

l

w


Functional Skills Mathematics€¦ · ©West Nottinghamshire College. 2 . Excellence in skills...

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