1. Measurement 2

2. Perimeter
The distance around a closed shape is its perimeter. (Like putting a fence around it).
Perimeter =
= 15cm

3. Example:
Sometimes we have to work out some missing lengths in order to get the perimeter.
eg:
13 cm
4 cm
6 cm
5 cm
7 cm
9 cm
Perimeter = 13
+ 4
+ 6
+ 5
+ 7
+ 9
= 44 cm

4. Circle - Circumference
The perimeter of a circle is called its circumference.
Circumference
C =  d

5. Example 1
C =  d
C =  x 8
= cm (2dp)

6. Example 2 radius = 3 cm  diameter = 6 cm C =  d C =  x 6
= cm (2dp)

7. Further Examples 3) Perimeter = Half circle circumference + 8 cm
= cm (2 dp) 4)
Perimeter = Quarter circle circumference
+ 3 cm + 3 cm
3 cm
= x 
= cm (2 dp)

8. Approximating Areas Area is approximately 18 m2 Counts as one

9. Rectangle: Area = b x h
Area = 8 x 6
= 48 cm2

10. HECTARE 1 hectare (1 ha) = 10000 m2
eg an area of 100m x 100m (2 football fields)
or 1000m (1km) x 10 m
or 10000m x 1 m
or 50m x 200m etc
100m
1000m
10m 1m
10000m

11. Triangle: Area = ½ x b x h Area = ½ x 10 x 6 = 30 cm2 Area = ½ x 5 x 8

13. b h

14. Parallelogram: Area = b x h
Start with a rectangle:
Area = 5.3 x 2
= 10.6 m2

16. Trapezium: Area = ½ ( a + b ) x h
a and b are the parallel sides
4 m
6 m
3 m
Area = ½ (4 + 6) x 3
= 5 x 3
= 15 m2

17. 4 m
6 m
3 m

19. actionmath
Trapezium example
A swimming pool is the shape of a trapezium (on its side)
25 m
shallow end
1 m
2 m
deep end
Area =
x 25
= m2

20. SONG - Tune of ‘Pop goes the Weasel’
Half the sum of the parallel sides
Times the distance between them;
That’s the way we calculate
The area of a trapezium
music

21. SONG - Tune of ‘Pop goes the Weasel’
Half the sum of the parallel sides
Times the distance between them;
That’s the way we calculate
The area of a trapezium

22. Composite Shapes
This could be calculated as a large rectangle with a piece cut out.
Large rectangle
Area = 10 x 6
= 60 X
cut out = 2 x 4
= 8
Area = 60 – 8
= 52 m2
example 2 

23. Composite Shapes
OR by dividing the shape into small rectangles and adding their areas together
4 m
6 m
We have to work out some lengths.
3 m
Area = (6 x 3) + (4 x 4) + (6 x 3)
= 52 m2

24. Composite Shapes Condt
7 cm
10 cm
4 cm
12 cm
Area 1 =
x 4 1
= 34 cm2 2
Area 2 =
x 10 x 12
= 60 cm2
Total Area =
NZ09: Pg 293 Ex 9D # 12,13
Alpha: Pg 183 Ex 11.5
= 94 cm2

25. Circle: Area = r2
Area =  r2
= π x 32
= cm2 ( 2dp)

26. example 2 Area = π r2 radius = 4 cm (half diameter) Area =  x 42
= cm2 (2dp)

27. Further Example 3) Area = circle area x  x r2 x  x 42
8 cm
x  x r2
x  x 42
= cm2 (2 dp)

28. Applications
Alpha: Pg 186 Ex 11.7
Alpha: Pg 195 Ex 12.3

29. Volume = Area of cross-section (end) x length
Volume = (5 x 4)
x 2
= 40 m3
5 cm
6 cm
10 cm
Volume = (½ x 5 x 6 )
x 10
= 150 cm3
Volume =  x 32
x 12
3 cm
12 cm
= cm3

30. Cubic Capacity
When we talk about volumes of liquids we often use the word capacity, rather than volume.
1000cc car engine has 1 litre capacity
ie 1000 cm3 holds 1 litre
 1000 cm3 holds 1000 mL
 cm3 holds 1 mL
1 m3 holds 1 kL
1 litre of water weighs 1 kg
 1000mL of water weighs 1000g
 1 mL of water weighs 1 g

31. Surface Area Hey man surface area is easy
The surface area of any solid can be found by adding the areas of each of its sides

32. Surface Area
The surface area is the same as the area of the net required to make the shape.

33. Example Find the surface of the box. Solution two sides of 8 by 1
base and top 8 by 5
front and back 5 by 1
Surface area = 2 x (8 x x x 1)
= 2 x 53
= 106 cm2