PERIMETER AND AREA - Weir Training



The Perimeter of a rectangle is the distance round the edge.

The Circumference of a circle is the distance around the edge.

The Diameter of a circle is the distance across the centre.

The Radius of a circle is the distance from the edge to the centre.

The distance around the edge of a circle has a special name. It is called the circumference.

The circumference is just like the perimeter but is only used when talking about circles.

If you know the radius or the diameter of a circle you can calculate its circumference.

The circumference is given by:

C = 2 π r

π is a special number and is always 3.14

Example 1

C = 2 π r

C = 2 × 3.14 × 5

Circumference = 31.4 cm

Example 2

Firstly we need to find the radius

The radius is half the length of the diameter

r = [pic]

r = 3 cm

So C = 2 π r

C = 2 × 3.14 × 3

= 18.84 cm

Exercise 1

Find the circumference of each of the following circles

1. 2. 3.

4. 5. 6.

NB. In a parallelogram the opposite sides are parallel.

Parallelogram area = b × h

A = b × h

Base (b)

Example

6 cm

8 cm

Area = b × h

= 8 × 6

= 48

Area = 48 cm2

Height (h) Triangle Area = Base × Height = b × h

2 2

Base (b) A = b × h

2

Trapezium Area = (a + b) × Height (h)

Height 2

(h)

Base (b) A = (a + b) × h

2

The area of a circle is given by

Area = π × (radius) 2

A = π r 2

Example

Area = π r 2

= π × 52

= 3.14 × 25

= 78.5 cm2

Remember that area always has square units. In this case since the radius is in cm, the area is in square centimetres (cm2)

Exercise 2

Find the area of the following circles

1. 2.

3. 4.

5. 6.

Exercise 3

For each of the following shapes find:

a) the perimeter or circumference

b) the area

1.

2.6 cm

4.3 cm

2.

5 cm

13 cm

3.

6 cm

5 cm 5 cm

10 cm

4.

Exercise 4

1. A circular pond has a diameter of 3.2 m.

a) What is the area of the pond?

b) What is the circumference?

2. A baseball stadium has a circular patch with a radius of 100 metres.

a) The groundsman is going to use a fertilizer and needs to know the area of the pitch. What is the area?

b) He also needs to know what the distance is all the way round. What is this dimension called and what is its value?

3. The diameter of the Earth at the equator is rather difficult to measure – we would need to dig a very long tunnel!! It is much easier to measure the circumference. The circumference of the Earth is 40,000 km. Can you calculate its diameter?

You could use a calculator and trial and improvement but make a note of each trial and the result.

The area of a composite shape is calculated by splitting the shape into separate shapes. The area of each one is then calculated and the areas are added together to find the total area. In examples below the shapes have been divided into two shapes.

Example 1

Area of shape A = 6 × 4 = 24 cm2

B = 3 × 2 = 6 cm2

Total Area = 24 + 6

= 30 cm2

Example 2

Area of shape C = [pic] (5 × 4) = 10 cm2

D = 4 × 3 = 12 cm2

Total Area = 10 + 12

= 22 cm2

Exercise 5

1. You need to order turf to make a new lawn as illustrated below

12·4 m

7·8 m

Find the total area in order that you can buy the correct amount of square metres of turf.

2. A triangular shape has to be painted on some scenery in an outdoor theatre. The triangle has a base of 6 m and a height of 7 m. To calculate the amount of paint required find the total area.

To calculate the area of the border

(area of large rectangle) - (area of small rectangle)

(12 x 9) - (8 x 5)

108 - 40 = 68m2

Exercise 6

1. A photographer has for sale three sizes of photographs with a border round

For each size, find the area of:

a) the photograph without its border

b) the photograph and border together

c) the border.

2. A rectangular garden is 18.5 m long and 12.4 m wide. It has a central lawn

10.8 m long and 6.5 m wide. Find the area of

a) the garden

b) the lawn

c) the border round the lawn

3. A postcard 14.2 cm by 9.5 cm has a stamp stuck in one corner. The stamp is 24 mm by 2 cm. Find the area of

a) the postcard

b) the stamp

c) the postcard not covered by the stamp.

4. A garden has a lawn 8.2 m long and 6·5 m wide. The border round the lawn is 1.5 m wide on each side as shown. Find

l

a) the area of the lawn

b) the length l of the garden

c) the width w of the garden

d) the total area of the garden

e) the area of the border w

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MSS1/L2.7

MSS1/L2.7

5 cm

MSS1/L2.7

6 cm

5 cm

2 cm

8 cm

2.4 cm

12 cm

16.4 cm

MSS1/L2.7

Height

(h)

MSS1/L2.7

(a)

[pic]

[pic]

MSS1/L2.7

5 cm

MSS1/L2.7

2 cm

4 cm

8 cm

1.4 cm

3.4 cm

18 cm

MSS1/L2.7

12 cm

4 cm

8.2 cm

MSS1/L2.7

MSS1/L2.8

A

7 cm

4 cm

B

C

D

3 cm

4 cm

MSS1/L2.8

[pic]

4·6 m

8·6 m

2 m border

MSS1/L2.8

NB. You must make all units the same before calculating c) i.e. convert mm to cm.

[pic][pic]

MSS1/L2.7

MSS1/L2.8

Workbook 12

Perimeter and Area

MSS1/L2.8

Definitions

Circumference of a circle

[pic]

The area of parallelogram

Area of a triangle

Area of a trapezium

[pic]

Area of a circle

[pic]

[pic]

[pic]

Composite shapes

Borders

12 m

[pic]

9 m

MSS1/L2.8

[pic]

10.5 cm

Z

13.5 cm

1 cm border

[pic]

X

13.5 cm

16.5 cm

2 cm border

[pic]

2 cm border

24.4 cm

19.85 cm

Y

[pic]

6 cm

4 cm

5 cm

[pic]

L2

Numeracy

______________

Application of Number

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