### Perimeter & Area - Nuffield Foundation

```Free-Standing Mathematics Activity
Perimeter
and area
© Nuffield Foundation 2011
How much lawn feed
do I need?
How much edging
do I need to go around
the lawn?
© Nuffield Foundation 2011
The gardener
needs to work
out the
perimeter and
the area of
the lawn
The perimeter of a shape is the total length of its sides
length
Perimeter of a rectangle
= length + width
+ length + width
width
length
5m
lawn
width
3m
Perimeter of this lawn
= 5 + 3 + 5 + 3 = 16 m
Is there another way to find the perimeter?
© Nuffield Foundation 2011
Area
Area measures the surface of something
1 metre
1 cm
1 m2
1 metre
1 square metre
© Nuffield Foundation 2011
1 cm
1
cm2
1 mm
1 mm 1 mm2
Area of a rectangular lawn
5 metres long
3 metres wide
The area is 15 square metres = 15 m2
Area of a rectangle = length × width
© Nuffield Foundation 2011
Area of rectangle = length × width
65 m
32 m
field
Area of field = 65 × 32
= 2080 m2
21 cm
page
© Nuffield Foundation 2011
30 cm
Area of the page = 30 × 21
= 630 cm2
To find the perimeter of this L-shaped room
What else is needed?
3m
1.5 m
4.5 m
2.2 m
3m
Perimeter
3 + 1.5 + 2.2 + 3
+ 5.2 + 4.5 = 19.4 m
5.2 m
© Nuffield Foundation 2011
To find the area of this L-shaped room
How can we do this?
3m
1.5 m
4.5 m
2.2 m
A
B
5.2 m
3m
Area of A = 4.5 × 3
= 13.5 m2
Area of B = 3 × 2.2
= 6.6 m2
Total area = 13.5 + 6.6 = 20.1 m2
© Nuffield Foundation 2011
To find the area of this L-shaped room
Another way
3m
A
1.5 m
4.5 m
Area of A = 3 × 1.5
= 4.5 m2
2.2 m
B
3m
Area of B = 5.2 × 3
5.2 m
Total area = 4.5 + 15.6 = 20.1 m2
© Nuffield Foundation 2011
= 15.6 m2
To find the area of this L-shaped room
Yet another way!
3m
Area of
large rectangle = 5.2 × 4.5
1.5 m
4.5 m
2.2 m
= 23.4 m2
3m
Area of
small rectangle = 2.2 × 1.5
5.2 m
Total area = 23.4 − 3.3 = 20.1 m2
© Nuffield Foundation 2011
= 3.3 m2
Which way was best?
At the end of the activity
•
•
•
•
•
What does the word ‘perimeter’ mean?
How do you find the perimeter of a shape?
What units are used for perimeters?
How do you find the area of a shape?
What units are used for areas?
• How would you find
the area of this
shape?
© Nuffield Foundation 2011
Car park
Play area Carpet
Mirror
surround
```