© Boardworks Ltd 2001 Menu MORE AREAS A. TRAPEZIA B. COMPOUND SHAPES C. CIRCLES.
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Transcript of © Boardworks Ltd 2001 Menu MORE AREAS A. TRAPEZIA B. COMPOUND SHAPES C. CIRCLES.
© Boardworks Ltd 2001
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MORE AREAS
A. TRAPEZIA
B. COMPOUND SHAPES
C. CIRCLES
© Boardworks Ltd 2001
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Areas 2 Menu
Trapezia
Compound ShapesCircles
Explanations
Introduction
Questions
A. TRAPEZIA
A1 A2 A3 A4 A5 A6 A7 A8
B. COMPOUND SHAPES
B1 B2 B3 B4 B5 B6 B7 B8
C. CIRCLES
C1 C2 C3 C4 C5 C6 C7 C8
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Pressing keys or clicking moves slides on.
Pressing P goes to previous slide.
SLIDE CONTROL WHEN IN PRESENTATION MODE
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Click on Menu button to return.
In presentation mode, right click, then ‘help’gives a full list of control options.
© Boardworks Ltd 2001
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What shapes can you spot?
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Some obvious ones?
Triangle
Rectangle
Semi - Circle?
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Did you see this one?
Trapezium
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COMPOUND AREASAreas made up of more than one shape?
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COMPOUND AREASAreas made up of more than one shape?
Did you spot this“arch” shape madeup of a semicircleand a rectangle?
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Area of a Trapezium
Area of Trapezium
= x ( sum of parallel sides ) x height12
“height” = perpendicular distance between the parallel sides
h
Area of Trapezium
= x (a + b) x h12
a
b
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5 cm
Area of Trapezium
= x ( sum of parallel sides ) x height
4 cm
Area of Trapezium
Area = 16 cm2
Area of a Trapezium
= x (3 + 5) x 412
12
3 cm
5 cm
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5 cm
Area of Trapezium
= x ( sum of parallel sides ) x height
7 cm
Area of Trapezium
Area = 30 cm2
Area of a Trapezium
= x (3 + 7) x 612
12
3 cm6 cm
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5 cm
Area of Trapezium
= x ( sum of parallel sides ) x height
6 cm
Area of Trapezium
Area = 21 cm2
Area of a Trapezium
= x (2 + 5) x 612
12
5 cm
2 cm
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5 cm
Area of Trapezium
= x ( sum of parallel sides ) x height
5 cm
Area of Trapezium
Area = 32.5 cm2
Area of a Trapezium
= x (5 + 8) x 512
12
8 cm
5 cm
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Area of a Compound Shape
3 x 4 = 12 cm2
5cm
6cm
2cm3cm
5 x 6 = 30cm2
4cm
Total = 12 + 30 = 42 cm2
Next Slide
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Area of a Compound Shape
Total = 36 + 18 = 54 cm2
6 x 6 = 36cm2
6cm
6cm
6cm 0.5 x 6 x 6 = 18cm2
Next Slide
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Area of a Compound Shape
Total = 70 - 14 = 56 cm2
10cm
7cm
4cm
Triangle 0.5 x 7 x 4 = 14 cm2
Rectangle 7 x 10 = 70 cm2
Next Slide
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Area of a Circle
3cm
A = r 2
A = 3.14 x 3 x 3
= 28.26 cm2
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Area of a Circle
5cm
A = r 2
A = 3.14 x 5 x 5
= 78.50 cm2
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Area of a Sector of a Circle
A = r 2
A = 3.14 x 3 x 3
= 28.26 cm2
Whole Circle
Divide by 2 = 14.13 cm2
3cm
Next Slide
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Area of a Sector of a Circle
A = r 2
A = 3.14 x 4 x 4
= 50.24 cm2
Whole Circle
Divide by 2 = 25.12 cm2
8cm
Next Slide
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Area of a Sector of a Circle
A = r 2
A = 3.14 x 8 x 8
= 200.96 cm2 8cm
Whole Circle
Divide by 4 = 50.24 cm2
Next Slide
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Area of a Sector of a Circle
A = r 2
A = 3.14 x 6 x 6
= 113.04 cm2
Whole Circle
Divide by 3 = 37.68 cm2
6cm
120o
Next Slide
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Area of a Sector of a Circle
A = r 2
A = 3.14 x 3.5 x 3.5
= 38.465 cm2
3.5 cm
Whole Circle
Divide by 4 = 9.62 cm2
Next Slide
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B C D20cm2A 40cm2 30cm2 96cm2
A1
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4cm
4cm
6cm
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20cm2A B C
A1
1
2 ( 6 + 4 ) x 4
6cm2 10cm2 8cm2
4cm
4cm
6cm
B C D 40cm2 30cm2 96cm2
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B C D 30cm2A 20cm2 40cm2 13cm2
A2
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5cm
2cm
6cm
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20cm2B
A21
2 ( 6 + 2 ) x 5
C D 30cm2A 40cm2 13cm2
5cm
2cm
6cm
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B C D66cm2A 24cm2 55cm2 33cm2
A3
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6cm
4cm
7cm
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33cm2D
A3
1
2 ( 7 + 4 ) x 6
B C24cm2 55cm2
6cm
4cm
7cm
66cm2A
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B C D30cm2A 60cm2 20cm2 24cm2
A4
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2cm4cm10cm
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A41
2 ( 4 + 2 ) x 10
30cm2A B C D60cm2 20cm2 24cm2
2cm4cm10cm
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B C D40cm2A 60cm2 30cm2 23cm2
A5
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3cm
11cm
9cm
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A5 1
2 ( 9 + 11 ) x 3
30cm2CB D40cm2A 60cm2 23cm2
3cm
11cm
9cm
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B C D35cm2A 40cm2 60cm2 70cm2
A6
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5cm
5cm
9cm
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A6
1
2 ( 9 + 5 ) x 5
35cm2A B C D40cm2 60cm2 70cm2
5cm
5cm
9cm
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B C D12.5cm2A 35cm2 50cm2 17.5cm2
A7
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2cm5cm
5cm
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A7
1
2 ( 5 + 2 ) x 5
17.5cm2DB C12.5cm2A 35cm2 50cm2
2cm5cm
5cm
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B C D36cm2A 24cm2 18cm2 30cm2
A8
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6cm
2cm
12cm
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A8 1
2 ( 12 + 6 ) x 2
18cm2CB D36cm2A 24cm2 30cm2
6cm
2cm
12cm
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B C D12cm2A 18cm2 24cm2 40cm2
B1
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3cm
2cm
4cm3cm
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B1
18cm2B C D12cm2A 24cm2 40cm2
3cm
2cm
4cm3cm
12cm2
6cm2
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B C D42cm2A 16cm2 33cm2 48cm2
B2
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4cm
6cm3cm
3cm
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B2
9cm2
33cm2C42cm2 16cm2 48cm2
4cm
6cm3cm
3cm
A B D42cm2A 16cm2 48cm2
24cm2
3cm
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B C D35cm2A 28cm2 16cm2 21cm2
B3
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4cm
3cm
2cm
2cm
3cm
9cm
2cm
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B3
12cm2
28cm2B
4cm
4cm2
3cm
2cm
2cm
12cm2
3cm
9cm
2cm
C D35cm2A 16cm2 21cm2
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B C D30cm2A 20cm2 32cm2 24cm2
B4
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4cm
4cm
4cm
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B4
16cm2
24cm2D
4cm
4cm
4cm 8cm2
B C30cm2A 20cm2 32cm2
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B C D28cm2A 35cm2 45cm2 42.5cm2
B5
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3cm
5cm
4cm
6cm
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B5
18cm2
28cm2A
3cm
5cm
4cm
6cm
6cm
B C D 35cm2 45cm2 42.5cm2
10cm22cm
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B C D36cm2A 18cm2 32cm2 24cm2
B6
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5cm
6cm
2cm
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B6
12cm2
24cm2DB C36cm2A 18cm2 32cm2
5cm
6cm
2cmOne Method
Rectangle = 30cm2
Triangle = 6cm2
Area = 30 - 6 = 24cm2
6cm
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B C D27cm2A 24cm2 45cm2 22.5cm2
B7
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9cm
5cm
1cm
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B7
9cm2
27cm2A B C D 24cm2 45cm2 22.5cm2
9cm
5cm
1cm
18cm2
4cm
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B C D15cm2A 29cm2 20cm2 21cm2
B8
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1cm
6cm
4cm
1cm
3cm
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B8
9cm2
20cm2C
5cm21cm
6cm
4cm
1cm
3cm
6cm2
15cm2 29cm2 21cm2B D15cm2A 29cm2 21cm2
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B C D9cm2A 18cm2 28cm2 81cm2
C1
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Approximate Area?
3cm
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28cm2CB D9cm2A 18cm2 81cm2
3cm
12cm2
A = r 2
A = 3.14 x 3 x 3 = 28.26 cm2
C1 Approximate Area?
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B C D2cm2A 3cm2 6cm2 6cm2
C2
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Approximate Area?
1cm
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C2
3cm2B
Approximate Area?
C D2cm2A 6cm2 6cm2
1cm C1
12cm2
A = r 2
A = 3.14 x 1 x 1 = 3.14 cm2
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6cmB C D6cm2A 18cm2 36cm2 13cm2
C3
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2cm
Approximate Area?
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C3
13cm2D
2cm
12cm2
A = r 2
A = 3.14 x 2 x 2 = 12.56 cm2
6cmB C6cm2A 18cm2 36cm2
Approximate Area?
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B C D16cm2A 25cm2 50cm2 90cm2
C4
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8cm
Approximate Area?
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C4
25cm2B C D16cm2A 50cm2 90cm2
8cm
12cm2
A = r 2
A = 3.14 x 4 x 4 = 50.24 cm2
Halve = 25.12
Approximate Area?
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B C D100cm2A 84cm2 56cm2 28cm2
C5
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6cm
Approximate Area?
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C5
28cm2DB C100cm2A 84cm2 56cm2
6cm
12cm2
A = r 2
A = 3.14 x 6 x 6 = 113.04 cm2
Divide by 4 = 28.26
Approximate Area?
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B C D9cm2A 28cm2 14cm2 50cm2
C6
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6cm
Approximate Area?
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C6
14cm2CB D9cm2A 28cm2 50cm2
6cm
12cm2
A = r 2
A = 3.14 x 3 x 3 = 28.26 cm2
Halve = 14.13
Approximate Area?
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B C D28cm2A 14cm2 9cm2 30cm2
C7
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3cm
120o
Approximate Area?
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C7
9cm2CB D28cm2A 14cm2 30cm2
3cm
120o12cm2
A = r 2
A = 3.14 x 3 x 3 = 28.26 cm2
Divide by 3 = 9.42
Approximate Area?
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B C D24cm2A 20cm2 78.5cm2 77cm2
C8
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5cm
Approximate Area?
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C8
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20cm2B C D24cm2A 78.5cm2 77cm2
5cm
12cm2
A = r 2
A = 3.14 x 5 x 5 = 78.5 cm2
Divide by 4 = 19.625
Approximate Area?