Numeracy
Application of Number
______________
L1
Workbook 12
Perimeter and Area
MSS1/L1.8
MSS1/L1.9
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L1.8,9
Perimeter
The perimeter of a rectangle is the distance around the edge (L + W + L + W)
L
W
W
L
Example 1
5 cm
Length = 5 cm
Width = 3 cm
3 cm
The perimeter = L + W+ L + W
or 2 L + 2 W (because there are two lengths and two widths)
perimeter = ( 2 × 5) + ( 2 × 3) cm
= 10 + 6 cm
= 16 cm
(Always remember to give the units in the same form as the question).
Example 2
A room is 4.2 m long and 3 m wide. What is the perimeter?
Perimeter = 4.2 + 3 + 4.2 + 3
= 14.4 m
Workbook 12
Level 1: Numeracy/Application of Number
2
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L1.8,9
Exercise 1
Find the perimeter of the following shapes
1.
2.
2m
6 cm
4m
8 cm
3.
4.
4.1 m
0.8 m
1.2 m
1.7 m
5.
6.
7 cm
3 cm
7 cm
5 cm
5 cm
3 cm
4 cm
4 cm
2 cm
Hint : for 5 and 6 just remember that the perimeter is simply the distance around the edge of the
shape.
Workbook 12
Level 1: Numeracy/Application of Number
3
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L1.8,9
Area
2
2
Area is a measurement of space. Area is 2-D and is measured in square units e.g. cm or m .
The area of a rectangle is given by the formula
or
Area = Length × Width
A
=L×W
Example 1
5 cm
3 cm
Length = 5 cm
Width = 3 cm
Answer
Area = length × width
=L×W
=5×3
There is a space for 15 × 1
square centimeters (1 cm2)
= 15 cm2
Notice that if the dimensions are given in cm then the area is always in cm 2 or square
centimetres.
Example 2
A wooden door is 1.9 m by 0.8 m. What is the area of the door?
Answer
Area = Length × Width
= 1.9 × 0.8
= 1.52 m2
Workbook 12
Level 1: Numeracy/Application of Number
4
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L1.8,9
Exercise 2
Find the area of each of the following shapes
1.
2.
4 cm
8m
3 cm
4m
3.
4.
3.1 cm
4.1 m
0.8 m
4.6 cm
NOTE: all the measurements must be in the same units i.e. all centimetre or all metres and then
the area is measured in square units (cm2 or m2).
Workbook 12
Level 1: Numeracy/Application of Number
5
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L1.8,9
Applying your knowledge to everyday situations
Exercise 3
1.
You need to re-glaze a window. The window frame is 1.25 m wide and 2.3 m long.
Find:
a)
b)
c)
2.
You need to buy plants for the flowerbed. The bed is 63.5 cm long by 41.5 cm wide.
Find:
a)
b)
3.
its exact area
its area to the nearest whole m2
You are offered a roll of furnishing fabric at a reduced cost. It should sell at £6.99 a
square metre but you can buy it for £1.20 per square metre. The material is 1.6 m
wide by 9.75 m long.
Find:
a)
b)
6.
its area
its perimeter
An organisation needs to re-carpet a straight corridor. The corridor measures 15.5 m
long by 1.25 m wide. To decide how many square metres of carpet is required.
Find:
a)
b)
5.
its exact area
its perimeter
You want to tile a table top. The top measures 2.4 m long by 1.25 m wide.
Find:
a)
b)
4.
the area of the window frame
the total cost of the glass if is £4.80 for each m 2
the perimeter of the window frame.
the total area of the roll
the cost of the whole roll
You need to replace a broken panel. The original panel is 54.5 cm long by 31.2 cm
wide.
Find:
a)
b)
Workbook 12
the exact area of the panel
the area of the panel to the nearest 100 cm 2
Level 1: Numeracy/Application of Number
6
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Measures, Shape and Space
Perimeter and Area
MSS1/L1.8,9
7.
A garage floor is 4.5 m wide and 8.25 m long.
Find:
a)
b)
8.
A flat roof is 13.6 m long and 5.25 m wide.
Find
a)
b)
c)
9.
d)
the area of the lawn (i) exactly (ii) to the nearest whole m 2
the cost of the turf, if each m2 costs 25 pence
the length of the perimeter (or edge) of the lawn (i) exactly (ii) to the nearest
whole metre
the cost of plastic edging if each metre length of it costs 15 pence.
A vegetable garden is 18.4m long and 15.6m wide.
Find:
a)
b)
c)
d)
11.
the area and its perimeter
the roof is covered with waterproof felt costing £2.75 per m 2 Find the cost of the
felt required for the whole roof.
the perimeter of the roof is fitted with a gutter costing £0.65 per metre length.
Find the cost of the guttering required.
A person decides to lay a rectangular lawn 21.5 m long and 8·4 m wide.
Find:
a)
b)
c)
10.
its area and its perimeter
the cost of painting it, if one square metre of special paint costs £4.40.
its exact area
its area to the nearest whole m2
its perimeter
the cost of fencing the perimeter, if a metre length of fence costs £2.45
A rectangular piece of ground is to be made into a car park 67.5 m long and 52.8 m
wide.
Find:
a)
b)
c)
d)
Workbook 12
the area of the car park
the cost of the tarmac required to surface it if one m2 of tarmac costs £2.75
the perimeter of the car park
the cost of the kerbstones around the perimeter, if a metre length costs 45
pence.
Level 1: Numeracy/Application of Number
7
© West Nottinghamshire College 2004