Numeracy
Application of Number
______________
L2
Workbook 12
Perimeter and Area
MSS1/L2.7
MSS1/L2.8
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.7
Definitions
The Perimeter of a rectangle is the distance round 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.
Workbook 12
Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.7
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
πr
is a special number and is always 3.14
Example 1
5 cm
C=2
πr
C = 2 × 3.14 × 5
Circumference = 31.4 cm
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Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.7
Example 2
6 cm
Firstly we need to find the radius
The radius is half the length of the diameter
6
r=
2
r = 3 cm
So
C=2
πr
C = 2 × 3.14 × 3
= 18.84 cm
Exercise 1
Find the circumference of each of the following circles
1.
2.
2 cm
3.
5 cm
8 cm
4.
5.
12 cm
6.
2.4 cm
16.4 cm
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Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.7
The area of parallelogram
NB. In a parallelogram the opposite sides are parallel.
Height
(h)
Parallelogram area = b × h
A=b×h
Base (b)
Example
6 cm
8 cm
Area = b × h
=8×6
= 48
Area = 48 cm2
Workbook 12
Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.7
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)
2
Height
(h)
Base (b)
Workbook 12
A = (a + b) × h
2
Level 2 Numeracy/Application of Number
6
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.7
Area of a circle
The area of a circle is given by
Area =
π × (radius) 2
A
π r2
=
Example
5 cm
Area =
=
π r2
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)
Workbook 12
Level 2 Numeracy/Application of Number
7
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.7
Exercise 2
Find the area of the following circles
1.
2.
2 cm
4 cm
3.
4.
1.4 cm
8 cm
5.
6.
3.4 cm
18 cm
Workbook 12
Level 2 Numeracy/Application of Number
8
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.7
Exercise 3
For each of the following shapes find:
a)
the perimeter or circumference
b)
the area
1.
2.6 cm
4.3 cm
2.
12 cm
5 cm
13 cm
3.
6 cm
4 cm
5 cm
5 cm
10 cm
4.
8.2 cm
Workbook 12
Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.7
Exercise 4
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 patch 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?
You could use a calculator and trial and improvement but make a note of each trial and
the result.
Workbook 12
Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.8
Composite shapes
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
examples below the shapes have been divided into two shapes.
6 cm
Example 1
4 cm
A
7 cm
4 cm
B
A = 6 × 4 = 24 cm2
Area of shape
B = 3 × 2 = 6 cm2
Total Area
= 24 + 6
= 30 cm2
Example 2
5 cm
C
3 cm
D
4 cm
Area of shape C =
D=
Total Area
1
2
(5 × 4)
= 10 cm2
4×3
= 12 cm2
= 10 + 12
= 22 cm2
Workbook 12
Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.8
Exercise 5
1.
You need to order turf to make a new lawn as illustrated below
12·4 m
4·6 m
7·8 m
8·6
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.
Workbook 12
Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.8
Borders
12 m
2 m border
9m
To calculate the area of the border
(area of large rectangle) - (area of small rectangle)
(12 x 9) - (8 x 5)
108 - 40
= 68m2
Workbook 12
Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.8
Exercise 6
1.
A photographer has for sale three sizes of photographs with a border round
Z
10.5 cm
1 cm border
13.5 cm
X
16.5 cm
2 cm border
13.5 cm
Y
19.85 cm
2 cm border
24.4 cm
For each size, find the area of:
a) the photograph without its border
b) the photograph and border together
c) the border.
Workbook 12
Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L2.8
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 stuck 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.
NB. You must make
all units the same
before calculating c)
i.e. convert mm to cm.
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
l
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
w
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Level 2 Numeracy/Application of Number
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© West Nottinghamshire College 2004