Perimeter and Area
Perimeter
and Area
Curriculum Ready
ACMMG: 196, 197, 216
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Perimeter
and AND
Area
PERIMETER
AREA
2
before
I used to think:
after
But now I think:
What do I know now that I didn’t know before?
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J 12
SERIES
TOPIC
1
Perimeter and Area
Basics
Perimeter of Shapes
7 cm
6 cm
4 cm
5 cm
Perimeter = 5 + 5 + 5 + 5
Perimeter = 4 + 4 + 7 + 7
= 4 ^5 h
Perimeter = 6 + 6 + 6 + 6
= 2 ^4 h + 2 ^ 7 h
= 20 cm
= 4^6 h
= 22 cm
= 24 cm
tricky
r
r
= 2rr
where r = 3.14f
3
r
r
4
Diameter
Circumference = 2rr
= 2r # 3 cm
= 2 # ^3.14...h # 3
= 18.8 cm (1
Perimeter of semicircle = ` 1 # Circumferencej + Diameter
2
= ` 1 # 2rr j + ^2r h
2
1
= # ^2 # r # 4 cmh + ^2 # 4 cmh
2
= 20.6 cm (1
2
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Perimeter and Area
Basics
Composite Shapes
4 cm
5 cm
Perimeter = 4 + 4 + 4 + 4 + 8 + 5 + 5
= 4 ^4 h + 8 + 2 ^5 h
= 34 cm
8 cm
8 cm
4 cm
6 cm
? cm
4 cm
12 cm
12 cm - 6 cm = 6 cm .
12
Radius of the top semicircle = 8 cm ' 2 = 4 cm
Radius of the bottom semicircle = 6 cm ' 2 = 3 cm
P
P = ^4 + 4 + 6 + 4h + top semicircle + bottom semicircle
P = 18 + ` 2r # 4 j + ` 2r # 3 j
2
2
P = 39.99... cm
= 40 cm
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3
Perimeter and Area
Questions
Basics
4
12
3
5
6
10
5
6
11
e
9
6.2
3 cm
5
13 cm
10.4 cm
4
J 12
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TOPIC
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Perimeter and Area
Questions
Basics
16
18
14
3
50 m
46 m
12 cm
5 cm
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J 12
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5
Perimeter and Area
Knowing More
Area of Shapes
l
h
b
b
l
Area = length # breadth
Area = length # length
= l2
=l#b
Area = 1 # base # height
2
1
= bh
2
y
h
r
x
b
Area = base # height
= bh
Area = 1 # product of diagonals
2
1
= xy
2
Area = rr2
b
r
x
r
r
h
y
a
Area = 1 h^sum of parallel sidesh
2
1
= h^ a + bh
2
6
J 12
SERIES
TOPIC
Area = 1 ^product of diagonalsh
2
1
= xy
2
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Area = 1 ^ Area of circleh
2
2
1
= rr
2
Perimeter and Area
Knowing More
3.4 cm
4.8 cm
2 cm
Rectangle: A = l # b
Square: A = l2
= ^3.4h2
= 4.8 # 2
= 9.6 cm2
= 11.56 cm2
12 cm
6 cm
9 cm
7 cm
16 cm
Trapezium: A = 1 h^a + bh
2
1
= ^7h^12 + 16h
2
Circle: A = rr2
= r # ^6h2
= 113.1 cm2 (1 d.p.)
= 98 cm2
35
10 cm
2
x
Kite: A = 1 ^product of diagonalsh
2
1
A = ^10 # xh
2
1
` 35 = ^10xh
2
` 5x = 35
` x = 7 cm
x
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J 12
SERIES
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7
Perimeter and Area
Knowing More
Area of Composite Shapes
20 m
24 m
13 m
20 m
h
24 m
13 m
=
+
r = 24 ' 2 = 12 m
2
A = 1 rr
2
2
= 1 r^12 h
2
= 226.19fm
+
A = l#b
h
h2 = 132 - 122 = 25
= 20 # 24
= 480 m2
`h=5
A = 1 bh
2
= 1 # 24 # 5
2
2
. 226 m ^nearest unith
2
= 60 m2
` Area of shape = 226 m2 + 480 m2 + 60 m2
= 766 m2
8
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Perimeter and Area
Questions
13
A
Knowing More
15
B
7
7
D
C
11
AC = 8
BD = 9
16
h
9.6
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9
Perimeter and Area
Questions
Knowing More
5
h
13
20
x = 7 cm
y = 10 cm
cm 2
x
x
y
10
J 12
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TOPIC
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Perimeter and Area
Questions
Knowing More
x
40 m
x.
1
1
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J 12
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11
Perimeter and Area
9
Questions
2
9 m2
12
J 12
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Knowing More
Perimeter and Area
Questions
Knowing More
4m
2
2
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J 12
SERIES
TOPIC
13
Perimeter and Area
Using Our Knowledge
Perimeter and Area of Quadrants
r
r
1
4
1
4
Arc = 1 # circumference
4
Arc = 1 # 2rr
4
Arc = rr
2
P = Arc + ^2 # radiush
P = rr + 2r
2
1
4
Area of Quadrant = 1 # Area of Circle
4
Area of Quadrant = 1 # rr2
4
2
Area of Quadrant = rr
4
14
J 12
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TOPIC
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Perimeter and Area
Using Our Knowledge
Perimeter and Area of Sectors
i.
r
i
i
i = 360c
r
i
360c
i
360c
Arc = i # circumference
360c
Arc = i # 2rr
360c
P = Arc + ^2 # radiush
P = c i # 2rr m + 2r
360c
i
360c
Area of Sector = i # Area of Circle
360c
Area of Sector = i # rr2
360c
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J 12
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15
Perimeter and Area
Using Our Knowledge
2
40c
4
= 40c
6
P = c i # 2rr m + 2r
360c
P = 40c # 2r^4h + 2^4h
360c
P = 1 # 8r + 8
9
P = rr + 2r
2
r ^6 h
P=
+ 2^6 h
2
P = 9.424f + 12
P = 21.424f
P = 10.792f
. 21.42 cm
. 10.79 cm
2
A = rr
4
r ^6 2 h
A=
4
A = i # rr2
360c
A = 40c # r^42h
360c
A = 28.274f
A = 1 # 16r
9
. 28.27 cm 2
A = 5.585f
. 5.59 cm 2
214 cm 2
1
A = 120c # rr2 = 214 cm2
360c
120c
` rr2 = 214 # 360c = 642
120c
` r2 = 642 ' r = 204.354f
` r = 204.354f = 14.295f
` r . 14.3 cm (1 decimal place)
16
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r
Perimeter and Area
Using Our Knowledge
Perimeter and Area of Ellipses
.
b
a
b
a
a
b
The
A = rab
P . 2r
a2 + b2
2
(a)
(b)
a = 12 cm and b = 6 cm
2
6
A = rab
12
A = r^12h^6h
= 226.194f
. 226.19 cm2 (2 decimal places)
2
2
P . 2r
a +b
2
2
= 2r
2
2
12 + 6 = 2r 90
2
= 59.607f
= 59.61 cm ^2 decimal placesh
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J 12
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17
Perimeter and Area
Questions
Using Our Knowledge
i
i
360c
i=
i=
45c
288c
e
i =
360c
i =
360c
i=
i=
324c
120c
i =
360c
h
i =
360c
9
35c
10
8
18
J 12
SERIES
TOPIC
130c
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Perimeter and Area
Questions
Using Our Knowledge
1
15
11
150c
55c
12
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19
Perimeter and Area
Questions
Using Our Knowledge
50
a
b
20
b
a
20
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Perimeter and Area
Thinking More
Working Backwards
100 cm 2
i
12
A = i # rr2
360c
i
i = 360c 2# A
rr
Make i
i = 360c # 100
r ^12h2
i
= 79.577...c
. 80c (nearest degree)
Word Problems
14
22
a = 22 cm
1
b = 14 cm
A = rab
A = r^22h^14h = 967.61f
. 967.6 cm2
i = 60c
32
2
i = 60c
A = 32 m2
A = i # rr2
360c
Make r
r=
A # 360c =
i#r
32 # 360c
60c # r
= 7.81764...
. 8m
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J 12
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21
Perimeter and Area
Thinking More
Composite Area
2
6
40c
5
16
=
-
-
A = i # rr2
360c
= 40c # r^22h
360c
= 1 # 4r
9
A = 1 # base # height
2
= 1 #5#2
2
semiminor axis = b = 6 = 3
2
semimajor axis = a = 16 = 8
2
= 5 cm2
A = rab
= r^8 h^3 h
= 1.396f cm2
= 75.398fcm2
=
-
-
= 75.398f - 5 - 1.396f
= 69.001f
. 69 cm2 (nearest cm)
22
J 12
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Perimeter and Area
Questions
i = 180c.
6
i
70
2
Thinking More
10
85
2
i = 135c.
P . 2r
a2 + b2
2
Make b
402
4
1
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J 12
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23
Perimeter and Area
Questions
i = 180c
180c
r
r
^i = 180ch .
24
J 12
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TOPIC
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Thinking More
Perimeter and Area
8
Questions
Thinking More
3
3
20
3
2
3
2
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J 12
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25
Perimeter and Area
Questions
50
50
15
60
80
26
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Thinking More
Perimeter and Area
Answers
Basics:
e
Knowing More:
16cm
28cm
30cm
28cm
39cm
24cm
Area . 23.1m2
l = 3m
Diameter = 2m
= 3m
7.8cm
Area heart . 9.14m2
31.2cm
Area unpainted = 6.86m2
Perimeter = 182m
Using Our Knowledge:
Distance = 733.54m
Perimeter = 37.85cm
Knowing More:
91cm2
e
36 cm2
i = 45c
1
8
i = 288c
4
5
i = 120c
1
3
i = 36c
h
1
6
91 cm2
l . 5cm
h = 12.8cm
l . 42cm
Area = 61.44cm2
h = 12cm
21cm
Area = 240cm2
60cm
Area . 154cm2
l . 23cm
Area = 35cm2
Area . 58.1cm2
43cm
Area . 176.7cm2
Area . 188.5cm2
x = 20 m
Area shaded . 628.3cm2
a = 25
b = 10
Area unshaded . 171.7cm2
Area . 785cm2
Perimeter . 120cm
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J 12
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27
Perimeter and Area
Answers
Thinking More:
Area of sector . 57cm2
i . 80c
r . 8cm
b.
P2 - a2
2r2
b . 90.4cm
Area of sector = rr2 i
360c
2
Area of sector = rr
2
Area . 196.35cm2
Area . 117.81cm2
Area striped . 3981.2 cm2
28
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Perimeter and Area
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