Transcript Quadrilaterals - mathsrevision

Simple Areas
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National 4
EF 1.2b
Definition : Area is “ how much space a shape takes up”
A few types of special Areas
Counting
Squares
Rectangle
Composite Area
Saturday, 18 July 2015
RAT.
Parallelogram
Any Type of Triangle
Rhombus and kite
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Trapezium
Starter Questions
National 4
EF 1.2b
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Q1.
18-Jul-15
Solve the equation below
a
x  21  32
o
Q2.
Find the missing angles
Q3.
Find the average of the numbers below
2,5,6,7
Q4.
Which is the better deal
75% of £240
or
o
b
50% of £362
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Area Counting Squares
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National 4
EF 1.2b
18-Jul-15
Learning Intention
1.
To explain area in terms
of counting squares.
Success Criteria
1. To understand the term
area.
2. Find the area by counting
squares.
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Area Counting Squares
National 4
EF 1.2b
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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 :
18-Jul-15
1cm
1cm
1cm2
( 1 square centimetre )
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Area Counting Squares
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National 4
EF 1.2b
18-Jul-15
Now try Exercise 1
Ch14 (page 163)
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Starter Questions
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National 4
EF 1.2b
Q1.
What is the time difference 09:28 and 11:55
Q2.
Explain why the solution to the 3x  21  9
equation is x = 10
Q3.
Convert 23metres to
(a) cm
(b)
mm
Q4.
The answer to the question is 180.
What is the question.
18-Jul-15
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Area of a Rectangle
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National 4
EF 1.2b
18-Jul-15
Learning Intention
1.
To come up with a formula
for the area of a
rectangle.
2. Use the formula to solve
problems.
Success Criteria
1. To be able to state area
formula for a rectangle.
2. Apply formula correctly.
(showing working)
3. Answer containing
appropriate units
Created by Mr. Lafferty Maths Dept.
Area of a Rectangle
National 4
EF 1.2b
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1 cm
B
B
L
L
L = length
L
B = Breadth
18-Jul-15
L
B
A
3
X
1
=
3
4
X
3
=
12
3
X
2
=
6
B
Area = length x breadth
A= L x B
Must learn formula !
Created by Mr. Lafferty Maths Dept.
Area of a Rectangle
National 4
EF 1.2b
Example
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Find the area of the rectangle
18-Jul-15
B = 2cm
L = 9cm
Area = Length x Breadth
A=LxB
A=9x2
2
A = 18 cm
Created by Mr. Lafferty Maths Dept.
Area of a Rectangle
Example
Find the length B of the rectangle opposite
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National 4
EF 1.2b
18-Jul-15
B cm A = 36cm
Area = Length x Breadth
A=LxB
36 = 12 x B
36
B=
12
B = 3cm
2
L = 12cm
Balancing
Method
Remember
units
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Area of a Rectangle
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National 4
EF 1.2b
18-Jul-15
Now try Exercise 2
Ch14 (page 167)
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Starter Questions
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National 4
EF 1.2b
Q1.
Calculate
576  9
o
110
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
Saturday, 18 July 2015
15% of £200
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12
Any Triangle Area
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National 4
EF 1.2b
Learning Intention
1.
To develop a formula for
the area of ANY triangle.
2. Use the formula to solve
problems.
Saturday, 18 July 2015
Created by Mr.Lafferty
Success Criteria
1. To know the formula for
the area of ANY triangle.
2. Apply formula correctly.
(showing working)
3. Answer containing
appropriate units
13
Any Triangle Area
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Demo
Saturday, 18 July 2015
h = vertical height
Sometimes
called the
altitude
h
b
1
Area  bh
2
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14
MTH 3-11b
Any Triangle Area
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Example 1 : Find the area of the triangle.
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1
Area  bh
2
6cm
8cm
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1
Area   8  6
2
Area  24cm 2
15
Any Triangle Area
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National 4
EF 1.2b
Example 2 : Find the area of the triangle.
Altitude h outside triangle this time.
1
Area  bh
2
10cm
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4cm
Area 
1
 4  10
2
Area  20cm 2
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16
Area of
ANY Triangle
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National 4
EF 1.2b
18-Jul-15
Now try Exercise 4
Ch14 (page 174)
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Starter Questions
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National 4
EF 1.2b
1
33 % of £270 = 90
3
Q1.
Why is
Q2.
What is the time difference 07:54 and 13:36
Q3.
Solve
Q4.
Convert 45.1 metres to
(a) cm
(b)
mm
Q5.
The answer to the question is 90.
What is the question.
18-Jul-15
5x  37  8
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Area of a Composite
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National 4
EF 1.2b
18-Jul-15
Learning Intention
1.
Made up of
Simple shapes
To use knowledge to find
area of more complicate
shapes.
Success Criteria
1. To be able to use
knowledge gained so far to
find the area of more
complicated shapes..
2. Show appropriate working.
Created by Mr. Lafferty Maths Dept.
Area of a Composite
National 4
EF 1.2b
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Calculate the area of this shape
9cm
Total Area = 72 + 30
= 102cm2
A=lxb
8cm
18-Jul-15
6cm
A=9x8
A=
A=lxb
72cm2
5cm
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A=6x5
A = 30cm2
Area of a Composite
National 4
EF 1.2b
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Calculate the area of this shape
8cm
10cm
6cm
18-Jul-15
12cm
Area of a Composite
National 4
EF 1.2b
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Calculate the area of this shape
18-Jul-15
Total Area = 80 + 24
= 104cm2
A=lxb
10cm
A = 8 x 10
A=lxb
A = 80cm2
A = 4 x 6 6cm
A =24cm2
8cm
4cm
Area of a Composite
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National 4
EF 1.2b
18-Jul-15
Calculate the area of this shape
Rectangle 1
16cm
A=lxb
5cm A = 16 x 5
A = 80cm2
5c
m
6cm
Rectangle 2
A=lxb
A=6x5
A = 30cm2
Created by Mr. Lafferty Maths Dept.
Total Area
= 80 + 30
2
=110cm
Area of a Composite
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National 4
EF 1.2b
18-Jul-15
Now try Exercise 5
Ch14 (page 176)
Created by Mr. Lafferty Maths Dept.
Starter Questions
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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
Saturday, 18 July 2015
a (b  c )
a = -2 , b = -4 c = 6
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25
Parallelogram Area
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National 4
EF 1.2b
Learning Intention
1.
To develop a formula for
the area of a parallelogram.
2. Use the formula to solve
problems.
Saturday, 18 July 2015
Created by Mr.Lafferty
Success Criteria
1. To know the formula for the
area of a parallelogram.
2. Apply formula correctly.
(showing working)
3. Answer containing
appropriate units
26
Parallelogram Area
National 4
EF 1.2b
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Important NOTE
h = vertical height
h
b
Parallelogram Area  b  h
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27
Parallelogram Area
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National 4
EF 1.2b
Example 1 : Find the area of parallelogram.
3cm
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Parallelogram Area  b  h
9cm
Area = 9  3
Area = 27cm
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2
28
Area of a
Parallelogram
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National 4
EF 1.2b
18-Jul-15
Now try
Extension Booklet
2E(a) (page 71)
Created by Mr.Lafferty Maths Dept
Starter Questions
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National 4
EF 1.2b
Q1.
Find the area of the triangle.
Q2.
Expand out 2w( w - 5) – 3w
Q3.
Calculate
3cm
4cm
(-3)+(-5)  2
Q4.
Find the LCM of the two numbers 4 and 6
Saturday, 18 July 2015
Created by Mr.Lafferty
30
Rhombus and Kite Area
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National 4
EF 1.2b
Learning Intention
1.
To develop a single
formula for the area of
ANY rhombus and Kite.
2. Use the formula to solve
problems.
Saturday, 18 July 2015
Success Criteria
1. To know the formula for the
area of ANY rhombus and
kite.
2. Apply formulae correctly.
(showing working)
3. Answer containing
appropriate units
Created by Mr.Lafferty
31
This part of
the rhombus
is half of the small
rectangle.
Area of a Rhombus
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National 4
EF 1.2b
Saturday, 18 July 2015
d
D
Rectangle Area = (D×d)
1
Rhombus Area = (D × d)
2
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32
Area of a Kite
Exactly the same process as the rhombus
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National 4
EF 1.2b
Saturday, 18 July 2015
d
D
Rectangle Area = (D×d)
1
Kite Area = (D × d)
2
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33
Rhombus and Kite Area
National 4
EF 1.2b
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Example 1 : Find the area of the shapes.
2cm
5cm
1
Rhombus Area  ( D  d )
2
1
Area = (5  2)
2
Area = 5cm 2
Saturday, 18 July 2015
4cm
9cm
1
Kite Area  ( D  d )
2
1
Area = (9  4)
2
Area = 18cm
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2
34
Area of a
Kite & Rhombus
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National 4
EF 1.2b
18-Jul-15
Now try
Extension Booklet
2E(b) (page 75)
Created by Mr.Lafferty Maths Dept
Starter Questions
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National 4
EF 1.2b
Q1.
Find the area of the parallelogram
8
7
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
Saturday, 18 July 2015
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36
Trapezium Area
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National 4
EF 1.2b
Learning Intention
1.
To develop a formula for
the area of a trapezium.
2. Use the formula to solve
problems.
Saturday, 18 July 2015
Created by Mr.Lafferty
Success Criteria
1. To know the formula for the
area of a trapezium.
2. Apply formula correctly.
(showing working)
3. Answer containing
appropriate units
37
Trapezium Area
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National 4
EF 1.2b
a cm
X
h cm
W
Saturday, 18 July 2015
Two triangles WXY and WYZ
Y
1
Area1  ah
2
1
2
b cm
Z
1
Area2  bh
2
1
1
Total Area  ah  bh
2
2
1
Total Area  (a  b)h
2
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38
Trapezium Area
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National 4
EF 1.2b
Example 1 : Find the area of the trapezium.
5cm
4cm
Saturday, 18 July 2015
1
Area  (a  b)h
2
1
Trapezium Area = (5  6)  4
2
6cm
Trapezium Area = 22cm2
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39
Area of a Trapezium
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National 4
EF 1.2b
18-Jul-15
Now try
Extension Booklet
6E (page 78)
Created by Mr.Lafferty Maths Dept