National 4 EF 1.2b Tuesday, 09 June 2015 Created by Mr.Lafferty Simple Areas Definition : Area is “ how much space a shape takes up” A few types of special.

National 4EF 1.2b

Tuesday 18 April 2023 Created by Mr.Lafferty

Simple AreasSimple Areas

Definition : Area is “ how much space a shape takes up”

A few types of special Areas

Rectangle

TrapeziumRhombus and kiteParallelogram

Any Type of Triangle

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RAT.CountingSquares

Composite Area

18 Apr 2023 Created by Mr. Lafferty Maths Dept.

Starter QuestionsStarter Questions

21 32x

Q1. Solve the equation below

Q2. Find the missing angles

Q3. Find the average of the numbers below

Q4. Which is the better deal

ao

bo

2,5,6,7

75% of £ 240

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50% of £ 362or

National 4 EF 1.2b

18 Apr 2023Created by Mr. Lafferty Maths

Dept.

Area Counting Area Counting SquaresSquares

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1.1. To understand the term To understand the term area.area.

1. To explain area in terms of counting squares.

2.2. Find the area by Find the area by counting squares.counting squares.

National 4 EF 1.2b


Dept.


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The area of a shape is simply defined by :

“the amount of space a shape takes up.”

Think of a square measuring 1 cm by 1cm we say it is :

1cm

1cm

1cm2

( 1 square centimetre )

National 4 EF 1.2b


Now try Exercise 1 Ch14 (page 163)

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National 4 EF 1.2b


Dept.

Starter QuestionsStarter Questionsw

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Q3. Convert 23metres to (a) cm (b) mm

Q2.

Q1. What is the time difference 09:28 and 11:55

Explain why the solution to the 3 21 9

equation is x = 10

x

Q4. The answer to the question is 180. What is the question.

National 4 EF 1.2b


Dept.

Area of a Area of a RectangleRectangle

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1.1. To be able to state area To be able to state area formula for a rectangle.formula for a rectangle.

1. To come up with a formula

for the area of a rectangle.

2. Use the formula to solve problems.

2.2. Apply formula correctly. Apply formula correctly. (showing working)(showing working)

3.3. Answer containing Answer containing appropriate unitsappropriate units

National 4 EF 1.2b


Dept.


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3 1

3

4 3

2

3

6

12

X =

X =X =

L AB

L

L

LB

B

B

L = length

B = Breadth

Must learn formula !

1 cm

Area = length x breadthA = L x B

National 4 EF 1.2b


Dept.


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Example

Find the area of the rectangle

L = 9cm

B = 2cm

Area = Length x BreadthA = L x BA = 9 x 2

A = 18 cm2

National 4 EF 1.2b


Dept.


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Example

Find the length B of the rectangle opposite

L = 12cm

B cm

Area = Length x Breadth

A = L x B

36 = 12 x B

Balancing Method

A = 36cm2

36B =

12

B = 3cmRemember

units

National 4 EF 1.2b


Dept.ww

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Area of a RectangleArea of a Rectangle


National 4 EF 1.2b

Tuesday 18 April 2023 12Created by Mr.Lafferty


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

15% of £ 200ww

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National 4 EF 1.2b

National 4EF 1.2b


Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. To know the formula for To know the formula for the area of the area of ANYANY triangle. triangle.

1. To develop a formula for the area of ANY triangle.




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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



2

18 6

224

Area

Area cm

6cm

8cm

Example 1 : Find the area of the triangle.

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1

2Area bh



14 10

2Area

10cm

4cm

Example 2 : Find the area of the triangle.

Altitude h outside triangle this time.

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220Area cm

National 4 EF 1.2b

1

2Area bh

18 Apr 2023 Created by Mr.Lafferty Maths Dept

Now try Exercise 4

Ch14 (page 174)

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Area of Area of ANYANY Triangle Triangle

National 4 EF 1.2b


Dept.

Starter QuestionsStarter Questionsw

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133 % of £ 270 = 90

3Q1. Why is

Q4. Convert 45.1 metres to (a) cm (b) mm

Q3.

Q2. What is the time difference 07:54 and 13:36

Solve 5 37 8 x

Q5. The answer to the question is 90. What is the question.

National 4 EF 1.2b


Dept.

Area of a Area of a CompositeComposite

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1.1. To be able to use To be able to use knowledge gained so far knowledge gained so far to find the area of more to find the area of more complicated shapes..complicated shapes..

1. To use knowledge to find area of more complicate shapes.

2.2. Show appropriate Show appropriate working.working.

Made up ofSimple shapes

National 4 EF 1.2b


Calculate the area of this shape

8cm

9cm

5cm

6cm

A = l x b

A = 9 x 8

A = 72cm2

A = l x b

A = 6 x 5

A = 30cm2

Total Area =

= 102cm2

72 + 30


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National 4 EF 1.2b

18 Apr 2023


10cm

12cm

8cm

6cm


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National 4 EF 1.2b

18 Apr 2023


10cm

6cm

8cm

4cm

A = l x b

A = 8 x 10

A = 80cm2

A = l x b

A = 4 x 6

A =24cm2

Total Area =

80 + 24

= 104cm2


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National 4 EF 1.2b



5cm

6cm

16cm

5cm

A = l x bA = l x b

A = 16 x 5A = 16 x 5

A = 80cmA = 80cm22

Rectangle 1Rectangle 1

Rectangle 2Rectangle 2

A = l x bA = l x b

A = 6 x 5A = 6 x 5

A = 30cmA = 30cm22

Total Total AreaArea = 80 + 30

=110cm2


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National 4 EF 1.2b



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National 4 EF 1.2b



Q1. 40% of £90

Q2. Show that there are 2880 minutes in 2 days

Q3. Expand 2( y - 3p) – 2y

Q4. Calculate

( ) a = -2 , b = -4 c = 6a b cww

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National 4 EF 1.2b

National 4EF 1.2b



1.1. To know the formula for To know the formula for the area of a the area of a parallelogram.parallelogram.

1. To develop a formula for the area of a parallelogram.




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Parallelogram AreaParallelogram Area


Parallelogram AreaParallelogram Area

b

Parallelogram Area b h

Important NOTE

h = vertical height

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h

National 4 EF 1.2b


Parallelogram AreaParallelogram AreaExample 1 : Find the area of parallelogram.

Parallelogram Area b h

Area = 9 32Area = 27cm

9cm

3cm

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National 4 EF 1.2b


Now try Extension Booklet

2E(a) (page 71)

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Area of a Area of a ParallelogramParallelogram

National 4 EF 1.2b


Q3. Calculate


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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National 4 EF 1.2b

National 4EF 1.2b



1.1. To know the formula for To know the formula for the area of the area of ANYANY rhombus rhombus and kite.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 units

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Rhombus and Kite AreaRhombus and Kite Area

National 4 EF 1.2b


Area of a RhombusArea of a Rhombus

1Rhombus Area= (D×d)

2

D

d

Rectangle Area = (D×d)

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This part ofthe rhombus

is half of the smallrectangle.


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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National 4 EF 1.2b


Rhombus and Kite Rhombus and Kite AreaArea

1Rhombus Area ( )

2D d

1Area = (5 2)

2

Example 1 : Find the area of the shapes.

5cm

2cm

2Area = 5cm

1Kite Area ( )

2D d

1Area = (9 4)

2

2Area = 18cm

9cm

4cm

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National 4 EF 1.2b



2E(b) (page 75)

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Area of a Area of a Kite & RhombusKite & Rhombus

National 4 EF 1.2b



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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National 4 EF 1.2b

National 4EF 1.2b



1.1. To know the formula for To know the formula for the area of a trapezium.the area of a trapezium.

1. To develop a formula for the area of a trapezium.




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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

National 4 EF 1.2b



1Trapezium Area = (5 6) 4

2

Example 1 : Find the area of the trapezium.

6cm

4cm

5cm

2Trapezium Area = 22cm

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1 ( )

2Area a b h

National 4 EF 1.2b



6E (page 78)

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Area of a TrapeziumArea of a TrapeziumNational 4 EF 1.2b

National 4 EF 1.2b Tuesday, 09 June 2015 Created by Mr.Lafferty Simple Areas Definition : Area is “ how much space a shape takes up” A few types of special.

Documents

b slide

x b national

length b

area formula

lafferty maths

term area

squares composite area

squares national