Measurement 2

Perimeter The distance around a closed shape is its perimeter. (Like putting a fence around it). Perimeter = 2 + 4 + 2 + 3 + 1 +3 = 15cm

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

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

Example 1 C =  d C =  x 8 = 25.13 cm (2dp)

Example 2 radius = 3 cm  diameter = 6 cm C =  d C =  x 6 = 18.85 cm (2dp)

Further Examples 3) Perimeter = Half circle circumference + 8 cm = 20.57 cm (2 dp) 4) Perimeter = Quarter circle circumference + 3 cm + 3 cm 3 cm = 6 x  + 3 + 3 = 10.71 cm (2 dp)

Approximating Areas Area is approximately 18 m2 Counts as one

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

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

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

b h

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

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

4 m 6 m 3 m

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 = 37.5 m2

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

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

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 

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

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 = 34 + 60 NZ09: Pg 293 Ex 9D # 12,13 Alpha: Pg 183 Ex 11.5 = 94 cm2

Circle: Area = r2 Area =  r2 = π x 32 = 28.27 cm2 ( 2dp)

example 2 Area = π r2 radius = 4 cm (half diameter) Area =  x 42 = 50.27 cm2 (2dp)

Further Example 3) Area = circle area x  x r2 x  x 42 8 cm x  x r2 x  x 42 = 25.13 cm2 (2 dp)

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

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 = 339.29 cm3

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  1 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

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

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

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 1 + 8 x 5 + 5 x 1) = 2 x 53 = 106 cm2