Page 171 - Mathematics Coursebook

18.1 Converting between units for area

18.1 Converting between units for area

1 mm

!e diagram shows three squares.
1 m

t !e "rst has a side length of 1 mm. 1 cm

t !e second has a side length of 1 cm.

t !e third has a side length of 1 m. 1 mm 1 cm 1 m

t !e "rst square has an area of 1 square millimetre (1 mm ). Not to scale

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t !e second has an area of 1 square centimetre (1 cm ).
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t !e third has an area of 1 square metre (1 m ).

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To convert between units of area you need to know the conversion factors.
Look at the square with a side length of 1 cm and area 1 cm . Area = 1 cm 2
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If you divide it up into squares with side length 1 mm
you get 10 × 10 = 100 of these smaller squares. 1 cm = 10 mm

!is shows that: 1 cm = 100 mm 2
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1 cm = 10 mm
You can do the same with the square with a side length Area = 1 m 2
of 1 m and area 1 m .
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If you divide it up into squares with side length 1 cm 1 m = 100 cm
you get 100 × 100 = 10 000 of these smaller squares.

!is shows that: 1 m = 10 000 cm 2
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1 m = 100 cm
Not to scale
Worked example 18.1

a What units for area would you use to measure the area of a football pitch?
b A shape has an area of 5 cm . What is the area of the shape, in square millimetres?
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a Square metres, m You would measure the length of a football pitch in metres, so the area
would be in square metres.
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b 5 × 100 = 500 mm 1 cm = 100 mm , so 5 cm would be 5 times as much.
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) Exercise 18.1

1 What units would you use to measure the area of:
a a postage stamp b a bank note c a tennis court d a cinema screen?

2 Copy and complete the following area conversions.
a 6 cm = mm b 7.2 cm = mm c 3 m = cm 2
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d 5.4 m = cm e 900 mm = cm f 865 mm = cm 2
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g 20 000 cm = m h 48 000 cm = m i 125 000 cm = m 2
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3 Is Maha correct? Explain your answer.
An area of 0.25 m is the same as 25 000 mm .
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170 18 Area, perimeter and volume