mth 3-11b tuesday, 19 august 2014 1created by mr.lafferty level 3 areas of simple shapes this...
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MTH 3-11b
Tuesday 11 April 2023 1Created by Mr.Lafferty
Level 3Level 3Areas of Simple ShapesAreas of Simple Shapes
This presentation will cover the formulae for the areas of various simple shapes.
It is aimed at students studying at level 3.
Where appropriate, follow up exercises are indicated
for consolidation purposes.
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MTH 3-11b
Tuesday 11 April 2023 2Created by Mr.Lafferty
Simple AreasSimple Areas
Definition : Area is “ how much space a shape takes up”
A few types of special Areas
Revision of Square, Rectangle and RAT.
TrapeziumRhombus and kite Parallelogram
Any Type of Triangle
Composite shapes
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MTH 3-11b
Tuesday 11 April 2023 3Created by Mr.Lafferty
Starter QuestionsStarter Questions
3 21 30x
Q1. Is the solution to the equation x = -3 Explain
Q2. Are the missing angles ao = 45o and bo = 55o
Q3. Explain why the mean is equal to 12
Q4. How many difference ways can you find
ao
bo
16, 9, 15,8
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MTH 3-11b
Tuesday 11 April 2023 4Created by Mr.Lafferty
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To remember the area To remember the area formula for the square, formula for the square, rectangle and RAT’s.rectangle and RAT’s.
1. To revise the basic areas including square, rectangles and RAT’s.
2.2. Apply formulae Apply formulae correctly. correctly.
(showing working)(showing working)3.3. Answer containing Answer containing appropriate unitsappropriate units
Revision of AreaRevision of Areaw
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MTH 3-11b
Tuesday 11 April 2023 5Created by Mr.Lafferty
Revision of AreaRevision of Area
2Area l l l 12
Area b h
l
l
Exercise 1 Teejay Page 101
Area l bl
b h
b
The Square The Rectangle The RAT
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MTH 3-11b
Tuesday 11 April 2023 6Created by Mr.Lafferty
Basic Simple AreasBasic Simple Areas
Definition : Area is “ how much space a shape takes up”
A few types of special Areas
Revision of Square, Rectangle and RAT.
TrapeziumRhombus and kite Parallelogram
Any Type of Triangle
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MTH 3-11b
Tuesday 11 April 2023 7Created by Mr.Lafferty
Starter QuestionsStarter Questions
576 9
Q1. Calculate
Q2. Are the missing angles 70o,40o,40o Explain
Q3. Is the HCF of 10 and 36 180 Explain.
Q4. Explain 2 ways of calculating
110o
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MTH 3-11b
Tuesday 11 April 2023 8Created by Mr.Lafferty
Any Triangle AreaAny Triangle Area
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To remember the formula To remember the formula for the area of for the area of ANYANY triangle. triangle.
1. To develop a formula for the area of ANY triangle.
2.2. Apply formula correctly. Apply formula correctly. (showing working)(showing working)
3.3. Answer containing Answer containing appropriate unitsappropriate units
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MTH 3-11b
Tuesday 11 April 2023 9Created by Mr.Lafferty
Any Triangle AreaAny Triangle Area
h
b
Sometimes called
the altitude
h = vertical height
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1
2Area bh
Demo
MTH 3-11b
Tuesday 11 April 2023 10Created by Mr.Lafferty
Any Triangle AreaAny Triangle Area
2
18 6
224
Area
Area cm
6cm
8cm
Example 1 : Find the area of the triangle.
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1
2Area bh
MTH 3-11b
Tuesday 11 April 2023 11Created by Mr.Lafferty
Any Triangle AreaAny Triangle Area
14 10
2Area
Exercise 2 Teejay Page 104
10cm
4cm
Example 2 : Find the area of the triangle.
Altitude h outside triangle this time.
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220Area cm
1
2Area bh
MTH 3-11b
Tuesday 11 April 2023 12Created by Mr.Lafferty
Q3. Calculate
Starter QuestionsStarter Questions
Q1. Find the area of the triangle.
Q2. Expand out 2w( w - 5) – 3w
Q4. Find the LCM of the two numbers 4 and 6
(-3)+(-5) 2
4cm
3cm
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MTH 3-11b
Tuesday 11 April 2023 13Created by Mr.Lafferty
Rhombus and Kite AreaRhombus and Kite Area
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To remember the To remember the formula for the area of formula for the area of ANYANY rhombus and kite. rhombus and kite.
1. To develop a single formula for the area of ANY rhombus and Kite.
2.2. Apply formulae Apply formulae correctly. correctly.
(showing working)(showing working)3.3. Answer containing Answer containing appropriate unitsappropriate unitsw
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MTH 3-11b
Tuesday 11 April 2023 14Created by Mr.Lafferty
Area of a RhombusArea of a Rhombus
1Rhombus Area= (D×d)
2
Rectangle Area = (D×d)D
d
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This part ofthe rhombus
is half of the smallrectangle.
MTH 3-11b
Tuesday 11 April 2023 15Created by Mr.Lafferty
Area of a KiteArea of a Kite
1Kite Area= (D×d)
2
D
d
Rectangle Area = (D×d)
Exactly the same process as the rhombus
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MTH 3-11b
Tuesday 11 April 2023 16Created by Mr.Lafferty
Rhombus and Kite Rhombus and Kite AreaArea
1Rhombus Area ( )
2D d
1Area = (5 2)
2
2Area = 5cm
Example 1 : Find the area of the shapes.
5cm
2cm
1Kite Area ( )
2D d
1Area = (9 4)
2
2Area = 18cm
9cm
4cm
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MTH 3-11b
Tuesday 11 April 2023 17Created by Mr.Lafferty
Rhombus and Kite Rhombus and Kite AreaArea
Exercise 3 Teejay Page 107
Example 2 : Find the area of the V – shape kite.
1Kite Area ( )
2D d
1Area = (7 4)
2
2Area = 14cm7cm
4cm
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MTH 3-11b
Tuesday 11 April 2023 18Created by Mr.Lafferty
Starter QuestionsStarter Questions
Q1. Is the area of the rhombus equal to 10.5cm2
Explain your answer.
Q2. Show that there are 2880 minutes in 2 days
Q3. Expand 2p( y - 3p) – 2py
Q4. Calculate
( ) a = -2 , b = -4 c = 6a b c
7cm
6cm
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MTH 3-11b
Tuesday 11 April 2023 19Created by Mr.Lafferty
Parallelogram AreaParallelogram Area
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To remember the formula To remember the formula for the area of a for the area of a parallelogram.parallelogram.
1. To develop a formula for the area of a parallelogram.
2.2. Apply formula correctly. Apply formula correctly. (showing working)(showing working)
3.3. Answer containing Answer containing appropriate unitsappropriate unitsw
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MTH 3-11b
Tuesday 11 April 2023 20Created by Mr.Lafferty
Parallelogram AreaParallelogram Area
Parallelogram Area b h
b
Important NOTE
h = vertical height
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h
MTH 3-11b
Tuesday 11 April 2023 21Created by Mr.Lafferty
Parallelogram AreaParallelogram Area
Exercise 4 Teejay Page 110
Example 1 : Find the area of parallelogram.
Parallelogram Area b h
Area = 9 32Area = 27cm
9cm
3cm
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MTH 3-11b
Tuesday 11 April 2023 22Created by Mr.Lafferty
Starter QuestionsStarter Questions
Q1. Find the area of the parallelogram
Q2. Is the HCF 6 and 24 24 Explain your answer.
Q3. Show that 11.5 % of 150 is 17.25
Q4. Simplify 3(h -2) + h(2 - 4h) = -4h2 + 6h - 6
7
8
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MTH 3-11b
Tuesday 11 April 2023 23Created by Mr.Lafferty
Trapezium AreaTrapezium Area
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To remember the formula To remember the formula for the area of a for the area of a trapezium.trapezium.
1. To develop a formula for the area of a trapezium.
2.2. Apply formula correctly. Apply formula correctly. (showing working)(showing working)
3.3. Answer containing Answer containing appropriate unitsappropriate units
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MTH 3-11b
Tuesday 11 April 2023 24Created by Mr.Lafferty
Trapezium AreaTrapezium Area
W
X Y
Z
1
2
a cm
b cm
h cm
Two triangles WXY and WYZ
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1 ( )
2Total Area a b h
1 1
2 2Total Area ah bh
21
2Area bh1
1
2Area ah
MTH 3-11b
Tuesday 11 April 2023 25Created by Mr.Lafferty
Trapezium AreaTrapezium Area
1Trapezium Area = (5 6) 4
2
Exercise 5 Teejay Page 112
Example 1 : Find the area of the trapezium.
6cm
4cm
5cm
2Trapezium Area = 22cm
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1 ( )
2Area a b h
MTH 3-11b
Tuesday 11 April 2023 26Created by Mr.Lafferty
Starter QuestionsStarter Questions
Q1. Find the area of the trapezium
Q2. Is the HCF for 4 and 12 equal to 2.Explain your answer.
Q3. Find 6.5% of 60
Q4. Is 3(f – 4) - 4f = 7f -12 Explain your answer
7
9
8
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MTH 3-11b
Tuesday 11 April 2023 27Created by Mr.Lafferty
Composite AreasComposite Areas
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To understand the term To understand the term composite.composite.
1. To show how we can apply basic area formulae to solve more complicated shapes. 2.2. To apply basic formulae To apply basic formulae
to solve composite to solve composite shapes.shapes.
3.3. Answer containing Answer containing appropriate unitsappropriate units
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MTH 3-11b
Tuesday 11 April 2023 28Created by Mr.Lafferty
Composite AreasComposite Areas
21 1Triangle Area = 6 5 15
2 2b h cm
2Rectangle Area = 3 4 12l b cm
We can use our knowledge of the basic areas to work out more complicated shapes.
4cm
3cm5cm
2Total Area = 15+12=27cm
6cm
Example 1 : Find the area of the arrow.
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MTH 3-11b
Tuesday 11 April 2023 29Created by Mr.Lafferty
Composite AreasComposite Areas
1Trapezium Area = ( )
2a b h
Trapezium Area - Triangle Area
1Triangle Area =
2bh
21= (10 8) 11 99
2cm
Exercise 6 Teejay Page 114
Example 2 : Find the area of the shaded area.
11cm
10cm
8cm
4cm21
= 4 11 222
cm
2Shaded Area = 99 - 22 77cm
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