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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