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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
18 Apr 2023Created by Mr. Lafferty Maths
Dept.
Area Counting Area Counting SquaresSquares
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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
18 Apr 2023 Created by Mr. Lafferty Maths Dept.
Now try Exercise 1 Ch14 (page 163)
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Area Counting Area Counting SquaresSquares
National 4 EF 1.2b
18 Apr 2023Created by Mr. Lafferty Maths
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
18 Apr 2023Created by Mr. Lafferty Maths
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
18 Apr 2023Created by Mr. Lafferty Maths
Dept.
Area of a Area of a RectangleRectangle
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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
18 Apr 2023Created by Mr. Lafferty Maths
Dept.
Area of a Area of a RectangleRectangle
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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
18 Apr 2023Created by Mr. Lafferty Maths
Dept.
Area of a Area of a RectangleRectangle
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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
18 Apr 2023Created by Mr. Lafferty Maths
Dept.ww
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Area of a RectangleArea of a Rectangle
Now try Exercise 2 Ch14 (page 167)
National 4 EF 1.2b
Tuesday 18 April 2023 12Created 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
15% of £ 200ww
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National 4 EF 1.2b
National 4EF 1.2b
Tuesday 18 April 2023 13Created by Mr.Lafferty
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.
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
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Any Triangle AreaAny Triangle Area
Tuesday 18 April 2023 14Created 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 18 April 2023 15Created 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
Tuesday 18 April 2023 16Created by Mr.Lafferty
Any Triangle AreaAny Triangle Area
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
18 Apr 2023Created by Mr. Lafferty Maths
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
18 Apr 2023Created by Mr. Lafferty Maths
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
18 Apr 2023 Created by Mr. Lafferty Maths Dept.
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
Area of a Area of a CompositeComposite
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National 4 EF 1.2b
18 Apr 2023
Calculate the area of this shape
10cm
12cm
8cm
6cm
Area of a Area of a CompositeComposite
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National 4 EF 1.2b
18 Apr 2023
Calculate the area of this shape
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
Area of a Area of a CompositeComposite
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National 4 EF 1.2b
18 Apr 2023 Created by Mr. Lafferty Maths Dept.
Calculate the area of this shape
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
Area of a Area of a CompositeComposite
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National 4 EF 1.2b
18 Apr 2023 Created by Mr. Lafferty Maths Dept.
Area of a Area of a CompositeComposite
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Now try Exercise 5 Ch14 (page 176)
National 4 EF 1.2b
Tuesday 18 April 2023 25Created by Mr.Lafferty
Starter QuestionsStarter Questions
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
Tuesday 18 April 2023 26Created by Mr.Lafferty
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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.
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
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Parallelogram AreaParallelogram Area
Tuesday 18 April 2023 27Created by Mr.Lafferty
Parallelogram AreaParallelogram Area
b
Parallelogram Area b h
Important NOTE
h = vertical height
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h
National 4 EF 1.2b
Tuesday 18 April 2023 28Created by Mr.Lafferty
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
18 Apr 2023 Created by Mr.Lafferty Maths Dept
Now try Extension Booklet
2E(a) (page 71)
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Area of a Area of a ParallelogramParallelogram
National 4 EF 1.2b
Tuesday 18 April 2023 30Created 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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National 4 EF 1.2b
National 4EF 1.2b
Tuesday 18 April 2023 31Created by Mr.Lafferty
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 rhombus rhombus and kite.and kite.
1. To develop a single formula for the area of ANY rhombus and Kite.
2. Use the formula to solve problems.
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
Tuesday 18 April 2023 32Created by Mr.Lafferty
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.
Tuesday 18 April 2023 33Created 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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National 4 EF 1.2b
Tuesday 18 April 2023 34Created by Mr.Lafferty
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
18 Apr 2023 Created by Mr.Lafferty Maths Dept
Now try Extension Booklet
2E(b) (page 75)
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Area of a Area of a Kite & RhombusKite & Rhombus
National 4 EF 1.2b
Tuesday 18 April 2023 36Created 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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National 4 EF 1.2b
National 4EF 1.2b
Tuesday 18 April 2023 37Created by Mr.Lafferty
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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.
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
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Trapezium AreaTrapezium Area
Tuesday 18 April 2023 38Created 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
National 4 EF 1.2b
Tuesday 18 April 2023 39Created by Mr.Lafferty
Trapezium AreaTrapezium Area
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