ALGEBRA - Nuffield Foundation
In this activity you will find the perimeter and area of rectangles
and shapes made from rectangles.
Student information sheet
Perimeter
The perimeter of a shape is the total length of its sides.
The perimeter of this rectangular lawn = 5 + 3 + 5 + 3 = 16 m
Think about
Are there any other ways of working out the perimeter?
Area
Area measures the surface of something, usually in square metres (m2), square centimetres (cm2) or square millimetres (mm2).
The area of this lawn is 15 m2.
(Each square has an area of 1 m2.)
Summary Perimeter of a rectangle = length + width + length + width
or (length + width) × 2
Area of a rectangle = length × width
Sometimes shapes are made from two or more rectangles.
Example
The diagram shows an L-shaped floor.
The perimeter of the floor
= 3 + 1.5 + 2.2 + 3 + 5.2 + 4.5 = 19.4 m
Think about
Where did the 1.5 and 2.2 come from?
How could you find the area of this floor?
The area can be split into two rectangles, A and B.
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
Think about
Are there any other ways of finding the area of the floor?
Do they give the same answer?
Why are the units m2?
Student worksheet
Try these
1. Each diagram shows the dimensions of a floor.
Find the perimeter and area of each floor.
2. Find the perimeter and area of each towel and the facecloth.
3 Find the perimeter and area of this £5 note.
4. Work out the perimeter and area of each field.
5. Find the perimeter and area of each room.
c)
6. Work out the perimeter and area of each shape.
Reflection
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 rectangle? What units are used for areas?
Describe how you would find the area of these shapes.
-----------------------
5 m
3 m
3 m
5 m
3 m
5.2 m
4.5 m
3 m
3 m
5.2 m
4.5 m
3 m
2.2 m
1.5 m
B
A
6 m
4 m
4.5 m
5 m
4.8 m
6.4 m
a)
b)
c)
50 cm
100 cm
Hand
towel
70 cm
140 cm
Bath towel
30 cm
Facecloth
26 cm
135 mm
70 mm
c)
62.5 m
96.2 m
a)
34 m
25 m
260 m
290 m
b)
6 m
6 m
7 m
b)
10 m
a)
4 m
2 m
6 m
3 m
d)
1.2 m
2.1 m
2.5 m
1.5 m
5.2 m
2 m
1.5 m
4 m
5 m
3.5 m
b)
38 mm
38 mm
16 mm
14 mm
24 mm
22 cm
22 cm
44 cm
44 cm
a)
75 mm
125 mm
75 mm
75 mm
75 mm
c)
Play area
Car park
Carpet
Mirror surround
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