Transcript Quadrilaterals - mathsrevision

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MTH 3-11b
Level 3
Areas 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.
Saturday, 18 July 2015
Created by Mr.Lafferty
1
Simple Areas
MTH 3-11b
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Definition : Area is “ how much space a shape takes up”
A few types of special Areas
Revision of Square, Rectangle and RAT.
Rhombus and kite
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Parallelogram
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Any Type of Triangle
Trapezium
Composite shapes
2
Starter Questions
MTH 3-11b
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Q1.
Is the solution to the equation x = -3 Explain
3x  21  30
Q2.
Q3.
Are the missing angles
ao = 45o and bo = 55o
a
o
b
o
Explain why the mean is equal to 12
16, 9, 15,8
Q4.
How many difference ways can you find
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40% of £240
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Revision of Area
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MTH 3-11b
Learning Intention
1.
To revise the basic areas
including square,
rectangles and RAT’s.
Saturday, 18 July 2015
Success Criteria
1. To remember the area
formula for the square,
rectangle and RAT’s.
2. Apply formulae correctly.
(showing working)
3. Answer containing
appropriate units
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Revision of Area
MTH 3-11b
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The Square
The Rectangle
l
b
l
Area  l  l  l
The RAT
h
l
2
Area  l  b
b
1
2
Area  b  h
Exercise 1 Teejay Page 101
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Basic Simple Areas
MTH 3-11b
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Definition : Area is “ how much space a shape takes up”
A few types of special Areas
Revision of Square, Rectangle and RAT.
Rhombus and kite
Saturday, 18 July 2015
Parallelogram
Created by Mr.Lafferty
Any Type of Triangle
Trapezium
6
Starter Questions
MTH 3-11b
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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
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15% of £200
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Any Triangle Area
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MTH 3-11b
Learning Intention
1.
To develop a formula for
the area of ANY triangle.
Saturday, 18 July 2015
Success Criteria
1. To remember the formula for
the area of ANY triangle.
2. Apply formula correctly.
(showing working)
3. Answer containing
appropriate units
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MTH 3-11b
Any Triangle Area
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Demo
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h = vertical height
Sometimes
called the
altitude
h
b
1
Area  bh
2
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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
10
Any Triangle Area
MTH 3-11b
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Example 2 : Find the area of the triangle.
Altitude h outside triangle this time.
10cm
1
Area  bh
2
Area 
4cm
1
 4  10
2
Area  20cm
Exercise 2 Teejay Page 104
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2
Starter Questions
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MTH 3-11b
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
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Rhombus and Kite Area
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MTH 3-11b
Learning Intention
1.
To develop a single
formula for the area of
ANY rhombus and Kite.
Saturday, 18 July 2015
Success Criteria
1. To remember the formula
for the area of ANY
rhombus and kite.
2. Apply formulae correctly.
(showing working)
3. Answer containing
appropriate units
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This part of
the rhombus
is half of the small
MTH 3-11b
rectangle.
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Area of a Rhombus
d
D
Rectangle Area = (D×d)
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1
Rhombus Area = (D × d)
2
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Exactly the same process as the rhombus
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MTH 3-11b
Area of a Kite
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d
D
Rectangle Area = (D×d)
1
Kite Area = (D × d)
2
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MTH 3-11b
Rhombus and Kite Area
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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
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4cm
9cm
1
Kite Area  ( D  d )
2
1
Area = (9  4)
2
Area = 18cm
2
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MTH 3-11b
Rhombus and Kite Area
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Example 2 : Find the area of the V – shape kite.
1
Kite Area  ( D  d )
2
1
Area = (7  4)
2
4cm
7cm
Area = 14cm
2
Exercise 3 Teejay Page 107
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Starter Questions
MTH 3-11b
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Q1.
Is the area of the rhombus
equal to 10.5cm2
Explain your answer.
6cm
7cm
Q2.
Show that there are 2880 minutes in 2 days
Q3.
Expand 2p( y - 3p) – 2py
Q4.
Calculate
Saturday, 18 July 2015
a (b  c )
a = -2 , b = -4 c = 6
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Parallelogram Area
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MTH 3-11b
Learning Intention
1.
To develop a formula for
the area of a parallelogram.
Saturday, 18 July 2015
Success Criteria
1. To remember the formula
for the area of a
parallelogram.
2. Apply formula correctly.
(showing working)
3. Answer containing
appropriate units
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Parallelogram Area
MTH 3-11b
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Important NOTE
h = vertical height
h
b
Parallelogram Area  b  h
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Parallelogram Area
MTH 3-11b
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Example 1 : Find the area of parallelogram.
3cm
Parallelogram Area  b  h
9cm
Area = 9  3
Area = 27cm
2
Exercise 4 Teejay Page 110
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Starter Questions
MTH 3-11b
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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
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Trapezium Area
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MTH 3-11b
Learning Intention
1.
To develop a formula for
the area of a trapezium.
Saturday, 18 July 2015
Success Criteria
1. To remember the formula
for the area of a trapezium.
2. Apply formula correctly.
(showing working)
3. Answer containing
appropriate units
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Trapezium Area
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MTH 3-11b
a cm
X
h cm
W
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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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Trapezium Area
MTH 3-11b
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Example 1 : Find the area of the trapezium.
5cm
4cm
1
Area  (a  b)h
2
1
Trapezium Area = (5  6)  4
2
6cm
Trapezium Area = 22cm2
Exercise 5 Teejay Page 112
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Starter Questions
MTH 3-11b
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Q1.
9
8
Find the area of the trapezium
7
Q2.
Is the HCF for 4 and 12 equal to 2.
Explain your answer.
Q3.
Find 6.5% of 60
Q4.
Is
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3(f – 4) - 4f = 7f -12 Explain your answer
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Composite Areas
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MTH 3-11b
Learning Intention
1.
To show how we can apply
basic area formulae to solve
more complicated shapes.
Saturday, 18 July 2015
Success Criteria
1. To understand the term
composite.
2. To apply basic formulae to
solve composite shapes.
3. Answer containing
appropriate units
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Composite Areas
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MTH 3-11b
We can use our knowledge of the basic areas
to work out more complicated shapes.
Example 1 : Find the area of the arrow.
Rectangle Area = l  b  3  4  12cm2
5cm
3cm
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4cm
6cm
Triangle Area =
1
1
b  h   6  5  15cm 2
2
2
Total Area = 15+12=27cm 2
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Composite Areas
MTH 3-11b
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Example 2 : Find the area of the shaded area.
8cm
Trapezium Area - Triangle Area
Trapezium Area =
11cm
1
= (10  8)  11  99cm 2
2
4cm
10cm
1
( a  b)  h
2
Triangle Area =
1
1
bh =  4  11  22cm 2
2
2
Shaded Area = 99 - 22  77cm2
Exercise 6 Teejay Page 114
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