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Area and Perimeter
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Area and Perimeter
ACMMG: 109, 159, 196, 216
Solutions
9HSERIES TOPIC
1ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
Mathletics Passport © 3P Learning
How does it work? Solutions Area and Perimeter
1 a
Page 3 questions
Page 4 questions
Area using unit squares
Area using unit squares
a
c
e
g
a
d
g
b
e
h
c
f
f
b
d
Area = ǁŚŽůĞƐƋƵĂƌĞƐ
= ƵŶŝƚƐ2
Area = ǁŚŽůĞ+ ŚĂůĨƐƋƵĂƌĞƐ
= m2 + 2
1# m2
= m2
Area = ǁŚŽůĞ+ ƋƵĂƌƚĞƌƐƋƵĂƌĞƐ
= ƵŶŝƚƐ2 + 4
1# ƵŶŝƚƐ2
= ƵŶŝƚƐ2
Area = ǁŚŽůĞ+ half +
ƋƵĂƌƚĞƌƐƋƵĂƌĞƐ
= ƵŶŝƚƐ2 + 2
1# ƵŶŝƚƐ2 + 4
1# ƵŶŝƚƐ2
= ƵŶŝƚƐ2
Area = ǁŚŽůĞ+ ƋƵĂƌƚĞƌƐƋƵĂƌĞƐ
= Đŵ2 + 4
1# Đŵ2
= Đŵ2
Area = ǁŚŽůĞ+ ŚĂůĨƐƋƵĂƌĞƐ
= ƵŶŝƚƐ2 + 2
1# ƵŶŝƚƐ2
= ƵŶŝƚƐ2
Area = ǁŚŽůĞƐƋƵĂƌĞƐ
= mm2
4 6
64
2
2
3 4 4
4 24
4
4
6
4
4
2
2
2
3 4 4
4 24
2
3
3
6
4.5
2 Area cm9 2= Area units12 2= Area m6 2=
Area mm4.5 2= Area units5 2=
Area km.12 5 2= Area cm14 2=
Area mm8 2=
2 ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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9HSERIES TOPIC
How does it work? Solutions Area and Perimeter
3
4
1
a
c
b
d
Page 4 questions
Page 7 questions
Area using unit squares
Perimeter using unit squares
Here are 42ƐŽůƵƟŽŶƐdŚĞƌĞĂƌĞŵŽƌĞ
a
b WĞƌŝŵĞƚĞƌ= + + +
ƵŶŝƚƐ
= ƵŶŝƚƐ
WĞƌŝŵĞƚĞƌ= + + +
ƵŶŝƚƐ
= ƵŶŝƚƐ
2
1 3 1 3
8
8
2 2 2
9HSERIES TOPIC
3ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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How does it work? Solutions Area and Perimeter
1
Page 7 questions
Page 8 questions
Perimeter using unit squares
Perimeter using unit squares
2
3
c
a
a
b
b c d
WĞƌŝŵĞƚĞƌ= + + +
+ +
ƵŶŝƚƐ
= ƵŶŝƚƐ
2
8
1 1 1 1 2
P = 12ƵŶŝƚƐP = 10ƵŶŝƚƐ P = 14ƵŶŝƚƐ P = 13ƵŶŝƚƐ
ǀĞŶƚŚŽƵŐŚƚŚĞƐŚĂƉĞƐĂůůŚĂǀĞƚŚĞƐĂŵĞĂƌĞĂƚŚĞLJĚŽŶŽƚĂůůŚĂǀĞƚŚĞƐĂŵĞƉĞƌŝŵĞƚĞƌůĞŶŐƚŚƐdŚŝƐƐŚŽǁƐƚŚĂƚƚŚĞƐŚĂƉĞƐǁŝƚŚƚŚĞƐĂŵĞĂƌĞĂǁŝůůŶŽƚŶĞĐĞƐƐĂƌŝůLJŚĂǀĞƚŚĞƐĂŵĞƉĞƌŝŵĞƚĞƌ ^ŽƚŚĞƉĞƌŝŵĞƚĞƌŝƐŶŽƚƌĞůĂƚĞĚƚŽƚŚĞĂƌĞĂŽĨƚŚĞƐŚĂƉĞ
4
P = 10ƵŶŝƚƐ
P = 11ƵŶŝƚƐ
P = 16ƵŶŝƚƐ
P = 17ƵŶŝƚƐ
P = 12ƵŶŝƚƐ
P = 13ƵŶŝƚƐ
P = 18ƵŶŝƚƐ
P = 19ƵŶŝƚƐ
P = 14ƵŶŝƚƐ
P = 15ƵŶŝƚƐ
P = 20ƵŶŝƚƐ
4 ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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9HSERIES TOPIC
Where does it work? Solutions Area and Perimeter
1
1
2
3
4
a
a
a
c
b
b
b
d
Area = # ƵŶŝƚƐ2
= ƵŶŝƚƐ2
Area = # ƵŶŝƚƐ2
= ƵŶŝƚƐ2
Area = # mm2
= mm2
Area = # m2
= m2
ůĞŶŐƚŚ
ůĞŶŐƚŚ
ůĞŶŐƚŚ
ůĞŶŐƚŚ
ǁŝĚƚŚ
ǁŝĚƚŚ
ǁŝĚƚŚ
ǁŝĚƚŚ
Area = # km2
= km2
. km2;ƚŽŶĞĂƌĞƐƚǁŚŽůĞŬŵ2)
ůĞŶŐƚŚ ǁŝĚƚŚ
Area = # Đŵ2
= Đŵ2
. Đŵ2;ƚŽŶĞĂƌĞƐƚǁŚŽůĞĐŵ2)
ůĞŶŐƚŚ ǁŝĚƚŚ
Page 10 questions
Page 12 questions
Area: Squares and rectangles
Area: Triangles
2 0.6
3
1.4 7
2 30
1.4 4.3
5
4 0.36
6
1.96 30.1
16
2 0.6
2 3.2
Length Area width
units units
units
The length of the rectangle is units7 .
28 4
7
2
'
'
`
=
=
=
Length of each side
units
121
11
=
=
Area = 21 # #
ƵŶŝƚƐ2
= ƵŶŝƚƐ2
Area = 21 # #
ƵŶŝƚƐ2
= ƵŶŝƚƐ2
ďĂƐĞ ďĂƐĞŚĞŝŐŚƚ ŚĞŝŐŚƚ
2 8
324
4 8
9HSERIES TOPIC
5ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
Mathletics Passport © 3P Learning
Where does it work? Solutions Area and Perimeter
Area = # Đŵ2
= Đŵ2
Area = # ƵŶŝƚƐ2
= ƵŶŝƚƐ2
10 2.2
Area = # # m2
= m2
Area = # # ƵŶŝƚƐ2
= ƵŶŝƚƐ2
Area = # # m2
= m237.5
10
13.5
Area = # # mm2
= mm2
Area = # # Đŵ2
= Đŵ2
2 a
a
a
c
b
b
b
d
Page 12 questions
Page 14 questions
Area: Triangles
Area: Parallelograms
48
12
10
5
4.5 4.6
450 10.12
6
14
84
8
7.5
4
4.5
12
e
21
21
21
21
21
1
2
3
Area m m
m
221 24 10
240 2
# # #=
=
Area mm mm
mm
. .
.
221 1 2 1 6
1 92 2
# # #=
=
6 ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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9HSERIES TOPIC
Where does it work? Solutions Area and Perimeter
Page 16 questions
Area of composite shapes
1 a
b
c
d
Area 1 = mm # mm
= mm2
Area 1 = # # m2
= m2
Area 1 = # Đŵ2
= Đŵ2
Area 1 = # # m2
= m2
`ŽŵƉŽƐŝƚĞĂƌĞĂ= + mm2
= mm2
`ŽŵƉŽƐŝƚĞĂƌĞĂ= + m2
= m2
`ŽŵƉŽƐŝƚĞĂƌĞĂ= - Đŵ2
= Đŵ2
`ŽŵƉŽƐŝƚĞĂƌĞĂ= - m2
= m2
Area 2 = mm # mm
= mm2
Area 2 = # m2
= m2
Area 2 = # # Đŵ2
= Đŵ2
Area 2 = # m2
= m2
4
0.5
6.5
0.5
16
24
13
20
4
55
4
4
2
11
0.5
16
24
13
20
20
79
9
16
4
55
4
4
4
6
2
8
8
5
2
5
4
2
2
2
9HSERIES TOPIC
7ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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Where does it work? Solutions Area and Perimeter
Page 17 questions
Page 19 questions
Area of composite shapes
Perimeter of simple shapes
2 a
b
c
d
Area Area of square area of triangle
cm cm cm cm
cm cm
cm
13 13 12 5 2
169 30
199
2 2
2
# # '
= +
= +
= +
=
^ h
Area Area of parallelogram area of triangle
m m m m
m m
m
. .
.
.
4 5 3 4 5 2
13 5 9
22 5
2 2
2
# #
= +
= +
= +
=
cm m and cm m300 3 200 2= =
Area Area of large square area of small square
mm mm mm mm
mm mm
mm
6 6 2 2
36 4
32
2 2
2
# #
= -
= -
= -
=
Area Area of rectangle area of square area of triangle
units units units units units units
units units units
units
5 10 5 5 5 6 2
50 25 15
90
2 2 2
2
# # # '
= + +
= + +
= + +
=
^ h
1 a
b
WĞƌŝŵĞƚĞƌ= ƵŶŝƚƐ+ ƵŶŝƚƐ+ ƵŶŝƚƐ
= ƵŶŝƚƐ
WĞƌŝŵĞƚĞƌ= 2 # mm + 2 # mm
= mm
15
9
40
30
17 8
6
8 ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
Mathletics Passport © 3P Learning
9HSERIES TOPIC
Where does it work? Solutions Area and Perimeter
Page 19 questions
Page 20 questions
Perimeter of simple shapes
Perimeter of simple shapes
2
3
c
a
a
b
b
c d
d WĞƌŝŵĞƚĞƌ= 2 # Đŵ+ Đŵ
= Đŵ
WĞƌŝŵĞƚĞƌ= # m
= m
1 4
11
20
27
5
5
Perimeter cm
cm
4 5.8
23.2
#=
=
Perimeter cm
cm
300 550 600
1450
` = + +
=
^ h Perimeter mm
mm780
2 225 2 165# #` = +
=
^ hm cm3 300= cm mm16.5 165=
Perimeter mm
mm
2 2.4 2 .1 6
8
# #= +
=
^ h
Perimeter m
m
3 15
45
#=
=
Perimeter m
m
. .
.
3 4 5 2 4
10 8
= + +
=
^ h
9HSERIES TOPIC
9ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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Where does it work? Solutions Area and Perimeter
Page 20 questions
Page 22 questions
Perimeter of simple shapes
Perimeter of composite shapes
4
a b c d m v
V
4.4 m
6.5 m
5.2 m
P = 18 m
1.6 m P = 12 m
P = 14 m
P = 24 m
9 m
P = 32 m
P = 12 m
8 m
2.4 m
3.5 m
380Đŵ
440Đŵ
2 m
7 m
650Đŵ
1.1 m
6 m
5 m
c
c
c
d
d
b
v
v
a
a
m
b
E
F
N
L
T
S
W
H
N
E T
R
G
Y
T W E N T Y
1
2
a
a
cb d
WĞƌŝŵĞƚĞƌ= # Đŵ
= Đŵ
a = 4Đŵ a = 1.8 mm a = 9 m a = 5.2Đŵ
b = 5Đŵ b = 2.2 mm b = 6 m b = 11.2Đŵ
5 9.8
49
10 ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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9HSERIES TOPIC
Where does it work? Solutions Area and Perimeter
Page 22 questions
Page 23 questions
Perimeter of composite shapes
Perimeter of composite shapes
2 b
c
d
Perimeter = 2 # a m + 2 # m
= m +
m
= m
Perimeter = 3 # mm +
mm +
mm
= mm
Perimeter = # 4.1 cm +
#
cm
= cm
2
16
12
12
4
24
2 3.8
72
20 16
4
3
4
a
c
b
d
Perimeter mm
mm
12 4
48
#=
=
Perimeter cm
cm
2 4.8 2 3.6 2 .
21.2
2 2# # #` = + +
=
^ hPerimeter km
km
3 1.2 2 .
.
1 5
6 6
# #` = +
=
^ h
Perimeter m
m
. . .
.
5 2 2 2 4 4 6 6
26 4
# #= + +
=
^ h
mm cm
mm cm
48 4.8
.22 2 2
=
=
m km1200 1.2=
m
1 1 2 3 4 5 6 7 8 9 9 1 10
11 10 9 8 7 6 5 4 3 2 1 132
+ + + + + + + + + + + +
+ + + + + + + + + + + =
Total perimeter of completed path = 132 m
Each new spiral arm increases by 1ĂŌĞƌĞĂĐŚƚƵƌŶŐŽŝŶŐŽƵƚ;ĞdžĐĞƉƚĨŽƌůĂƐƚǀĞƌƟĐĂůĂƌŵͿ^ƚĂƌƟŶŐĂƚƚŚĞĚŽƚĂŶĚǁŽƌŬĚŽǁŶƚŚĞŶĂŶƟͲĐůŽĐŬǁŝƐĞŽŶƚŚĞǁĂLJŽƵƚĂŶĚƚŚĞŶĐůŽĐŬǁŝƐĞŽŶƚŚĞǁĂLJďĂĐŬŝŶƚŽƚŚĞĐĞŶƚƌĞ
9HSERIES TOPIC
11ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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Where does it work? Solutions Area and Perimeter
Page 24 questions
Page 26 questions
Perimeter of composite shapes
Simple word problems involving area and perimeter
5
1
a
b
c
Perimeter cm
cm
5 3
15
#=
=
^ŵĂůůĞƐƚƉŽƐƐŝďůĞƉĞƌŝŵĞƚĞƌ= 18ƵŶŝƚƐ
>ĂƌŐĞƐƚƉŽƐƐŝďůĞƉĞƌŝŵĞƚĞƌ= 40ƵŶŝƚƐ
dƌLJƚŽŵĂŬĞĂƐŵĂŶLJƐŝĚĞƐĂƐƉŽƐƐŝďůĞƚŽƵĐŚŝŶŐĞĂĐŚŽƚŚĞƌ ǁŚŝĐŚƌĞĚƵĐĞƐƚŚĞŶƵŵďĞƌŽĨƐŝĚĞƐƚŚĂƚĂƌĞĐŽƵŶƚĞĚĨŽƌƚŚĞƉĞƌŝŵĞƚĞƌ
DĂŬŝŶŐĞĂĐŚƐŚĂƉĞũŽŝŶĞĚƚŽƚŚĞŽƚŚĞƌďLJŽŶĞƐŝĚĞŽŶůLJ ǁŚŝĐŚŝŶĐƌĞĂƐĞƐƚŚĞŶƵŵďĞƌŽĨƐŝĚĞƐƚŚĂƚŵƵƐƚĐŽƵŶƚĞĚĨŽƌƚŚĞƉĞƌŝŵĞƚĞƌ
12 ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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9HSERIES TOPIC
Where does it work? Solutions Area and Perimeter
Page 26 questions
Page 27 questions
6LPSOHZRUGSUREOHPVLQYROYLQJDUHDDQGSHULPHWHU
6LPSOHZRUGSUREOHPVLQYROYLQJDUHDDQGSHULPHWHU
2
3
4
^ŚĂƉĞ1 ^ŚĂƉĞ2
WĞƌŝŵĞƚĞƌ= 10ƵŶŝƚƐ WĞƌŝŵĞƚĞƌ= 8ƵŶŝƚƐ
dŚĞĂƌĞĂŽĨďŽƚŚƐŚĂƉĞƐŝƐƚŚĞƐĂŵĞďƵƚƚŚĞƉĞƌŝŵĞƚĞƌƐĂƌĞĚŝīĞƌĞŶƚdŚŝƐƐŚŽǁƐƚŚĂƚƚŚĞƌĞŝƐŶŽƌĞůĂƟŽŶƐŚŝƉďĞƚǁĞĞŶƚŚĞĂƌĞĂĂŶĚƚŚĞƉĞƌŝŵĞƚĞƌŽĨĂƐŚĂƉĞ
4.2 m
1 m
2 m4 m
8 m
64 m
32 m 16 m 8 m
Height of triangle m
m
5 4.2
21
#=
=
Area of triangle m m
m
4.2 21
.
2
44 1 2
#` '=
=
^ h
a
a
b
b
1
1 3
2 4
23
4
Perimeter m m
m
: 2 1 2 64
130
# #= +
=
Perimeter m m
m
: 2 4 2 16
40
# #= +
=
Perimeter m m
m
: 2 2 2 32
68
# #= +
=
Perimeter m m
m
: 4 8
32
#=
=
`ŇŽŽƌƉůĂŶ 1 ŚĂƐƚŚĞůĂƌŐĞƐƚƉĞƌŝŵĞƚĞƌ
9HSERIES TOPIC
13ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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Where does it work? Solutions Area and Perimeter
Page 27 questions
Page 28 questions
6LPSOHZRUGSUREOHPVLQYROYLQJDUHDDQGSHULPHWHU
6LPSOHZRUGSUREOHPVLQYROYLQJDUHDDQGSHULPHWHU
4
5
c
d
a
EŽŇŽŽƌƉůĂŶ 1 ǁŽƵůĚŶŽƚďĞĂŐŽŽĚĐŚŽŝĐĞtŚŝůĞŝƚŵĞĞƚƐƚŚĞƌƵůĞŽĨŚĂǀŝŶŐƚŚĞůĂƌŐĞƐƚƉŽƐƐŝďůĞƉĞƌŝŵĞƚĞƌ ŝƚǁŽƵůĚďĞǀĞƌLJůŽŶŐĂŶĚƚŽŽŶĂƌƌŽǁĨŽƌŵŽƌĞƚŚĂŶŽŶĞƉĞƌƐŽŶƚŽǁĂůŬƚŚƌŽƵŐŚĂƚĂƟŵĞ
Number of stamps that fit width cm12.5 .52
5
'=
=
Area of stamp cm
cm
2.5 .
8.75
3 5
2
#=
=
Area of envelope cm
cm
. .
.
12 5 24 5
306 25 2
#=
=
Length of parallelogram m
m
2 34
68 2
#=
=
Therefore length of fence long side short side
m m
m
2 2
2 68 2 34
204
# #
# #
= +
= +
=
Length of each side of the square area m
m
204 4
51
` '=
=
cm cm
stamps were needed.
306.25 8.75 35
35
2 2` '
`
=
Number of stamps that fit length cm. .524 5 3
7
'=
=
Tota number of stamps that fit
stamps
5 7
35
#` =
=
OR
`ĂĐŚƐŝĚĞŽĨƚŚĞŶĞǁƐƋƵĂƌĞĂƌĞĂǁŝůůďĞ51ŵůŽŶŐ
14 ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
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9HSERIES TOPIC
Where does it work? Solutions Area and Perimeter
Page 28 questions
6LPSOHZRUGSUREOHPVLQYROYLQJDUHDDQGSHULPHWHU
5
6
b
b
a
Parallelogram area m m
m
68 30
2040 2
#=
=
Area of each brick cm cm
cm
28 16
448 2
#=
=
Perimeter Brick length Half brick length brick width
cm cm cm
cm cm cm
cm
10 8 10
28 10 14 8 16 10
280 112 160
552
# #
# # #
#= + +
= + +
= + +
=
Square area m m
m
51 51
2601 2
#=
=
Total area cm
cm
25
11200
448
2
#` =
=
`dŚĞŶĞǁƐƋƵĂƌĞƐŚĂƉĞǁŝůůƐƵƌƌŽƵŶĚŵŽƌĞĂƌĞĂ;ĂŶĞdžƚƌĂ m561 2ƚŽďĞĞdžĂĐƚͿ
`dŚĞƌĞǁŝůůďĞũƵƐƚĞŶŽƵŐŚƉĂŝŶƚƚŽĐŽǀĞƌƚŚĞƐŝĚĞŽĨƚŚĞǁĂůů;ǁŝƚŚ cm300 2 ƚŽƐƉĂƌĞͿ
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9HSERIES TOPIC
15ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
Mathletics Passport © 3P Learning
What else can you do? Solutions Area and Perimeter
bArea = + #
' 2 km2
= km2
Area = + #
' 2 m2
= m2
WĞƌŝŵĞƚĞƌ= km WĞƌŝŵĞƚĞƌ= m
Page 30 questions
Page 32 questions
Rhombus and Kite shapes
1
2
3
a
a
a
b
b
b
Area = # '
Đŵ2
= Đŵ2
Area = # #
21
mm2
= mm2
WĞƌŝŵĞƚĞƌ= 2 # + 2 # Đŵ
= Đŵ
WĞƌŝŵĞƚĞƌ= # mm
= mm
18 1.8
468
53 4.5
243 15.3
110 27
1 12.59 1.8
2.16
112 14.4
52 2.4
41 415 3.6
2
Perimeter m m
m
4 9 2 14
64
# #= +
=
Area cm
cm
15 2
135
5 8 5 2
2
# '= + +
=
^ h
Perimeter cm cm cm
cm
5.1 4 3.4 2 6.5
31.7
# #= + +
=
Area mm
mm
. . . 2.4 2
24.12
2 4 1 2 4 14 3 2
2
# '= + + +
=
^ h
Area Area of rhombus area of kite
m m
m
2 21 16 230 16
240 168
408
2 2
2
# #' '
= +
= +
= +
=
^ ^h h
a1
2
Trapeziums
16 ƌĞĂĂŶĚWĞƌŝŵĞƚĞƌ^ŽůƵƟŽŶƐ
Mathletics Passport © 3P Learning
9HSERIES TOPIC
What else can you do? Solutions Area and Perimeter
3
Page 32 questions
Page 33 questions
170Đŵ= 1.7ŵĂŶĚ240Đŵ= 2.4 m
Area Area Area
m m
m m
m
. . 1.7 2 . . 2.4 2
. .
.
33 4 2 4 16 7 2 4
30 43 22 92
53 35
2 2
2 2
2
# #' '
= +
= + + +
= +
=
^ ^h h1 2
Perimeter m m m
m
33.4 2 16.7 3 2.4
74
# #= + +
=
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Trapeziums
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Area and Perimeter
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