© 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


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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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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


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


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


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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Total = 36 + 18 = 54 cm2

6 x 6 = 36cm2

6cm

6cm

6cm 0.5 x 6 x 6 = 18cm2

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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

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A = r 2

A = 3.14 x 4 x 4

= 50.24 cm2

Whole Circle


8cm

Next Slide


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A = r 2

A = 3.14 x 8 x 8

= 200.96 cm2 8cm

Whole Circle


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A = r 2

A = 3.14 x 6 x 6

= 113.04 cm2

Whole Circle


6cm

120o

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A = r 2

A = 3.14 x 3.5 x 3.5

= 38.465 cm2

3.5 cm

Whole Circle


Next Slide


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B C D20cm2A 40cm2 30cm2 96cm2

A1

Hit key or click for ANSWER

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


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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A3


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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A4


2cm4cm10cm


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A41

2 ( 4 + 2 ) x 10

30cm2A B C D60cm2 20cm2 24cm2

2cm4cm10cm


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A5


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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A6


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


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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A8


6cm

2cm

12cm


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A8 1

2 ( 12 + 6 ) x 2


6cm

2cm

12cm


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B1


3cm

2cm

4cm3cm


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B1

18cm2B C D12cm2A 24cm2 40cm2

3cm

2cm

4cm3cm

12cm2

6cm2


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B2


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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B3


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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B4


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


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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B6


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


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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B8


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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C1


Approximate Area?

3cm


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3cm

12cm2

A = r 2

A = 3.14 x 3 x 3 = 28.26 cm2

C1 Approximate Area?


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C2


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


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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C4


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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C5


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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C6


6cm

Approximate Area?


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C6


6cm

12cm2

A = r 2

A = 3.14 x 3 x 3 = 28.26 cm2

Halve = 14.13

Approximate Area?


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C7


3cm

120o

Approximate Area?


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C7


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


5cm

Approximate Area?


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C8


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?

© boardworks ltd 2001 menu more areas a. trapezia b. compound shapes c. circles

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