Dŵr y Felin Comprehensive School
Perimeter, Area and
Volume Methodology
Booklet
Perimeter, Area & Volume
Perimeters, Area & Volume are key concepts within the Shape & Space aspect of
Mathematics. Pupils understanding of these concepts can be reinforced in subjects that
require the use of spatial awareness.
Throughout these topics the following skills are inherent
Strand
Developing Numerical reasoning
Element
Identify processes and connections
Learners are able to
• Transfer mathematical skills across the curriculum in a variety of contexts and everyday
situations
• Select, trial and evaluate a variety of possible approaches and break complex problems into a
series of tasks
• Prioritise and organise the relevant steps needed to complete the task or reach a solution
• Choose an appropriate mental or written strategy and know when it is appropriate to use a
calculator
• Identify, measure obtain required information to complete the task
• Identify what further information might be required and select what information is most
appropriate
• Select appropriate mathematics and techniques to use
• Estimate and visualise size when measuring and use the correct units
Strand
Developing Numerical reasoning
Element
Represent and communicate
Learners are able to
• Explain results and procedures precisely using appropriate mathematical language
• Use appropriate notation, symbols and units of measurements, including compound measures
Strand
Developing Numerical reasoning
Element
Review
Learners are able to
• Select and apply appropriate checking strategies
• Interpret answers within the context of the problem and consider whether answers, including
calculator, analogue and digital displays, are sensible
Perimeter
Key Teaching Point
Perimeter is the distance around the outside of a shape. Pupils need to ‘add up’ all the
measurements.
Strand
Using Measuring Skills
Element
Length, weight/mass, capacity
Learners are able to
• Find perimeters of shapes with straight sides (7MS1)
Key Features
•
•
•
•
Set out calculations in a structured way
Pupils should be encouraged to check their work thoroughly.
Answers must include units - mm, cm or metres.
Pupils need to ensure all measurements used are in the same units.
Common Misconceptions
• Errors in basic mental addition
• Missing out some of the measurements
• Ignoring any lengths that are not given instead of calculating their measurements first
before finding the perimeter.
Examples
1. Find the perimeter of this square
Perimeter = 3 + 3 + 3 + 3
=12cm
When shapes are drawn on
cm squared paper pupils
can count around the
outside or be encouraged to
identify each length and
then add up.
2. Calculate the perimeter of this rectangle
9cm
Perimeter = 3 + 9 + 3 + 9 = 24cm
3cm
The opposite sides
of a rectangle are
equal in length.
3.
Calculate the perimeter of this regular hexagon
2cm
Perimeter = 2 + 2 + 2 + 2 + 2 + 2 = 12cm
OR
Perimeter = 2 x 6 = 12cm
Area
If a shape is
regular then all the
sides are the same
length
Key Teaching Point
The area of a shape is the space inside. The topic would initially be introduced with shapes
drawn on cm squared paper and pupils will just need to count the squares inside a shape.
This will then lead on to the following formulae being used.
length
Area of a rectangle = length x width
width
Area of a triangle = ½ x base x height
height
(where the height is perpendicular with the base i.e.
meets at a right angle)
base
Strand
Using Measuring Skills
Element
Area and volume
Learners are able to
• Use formulae for the area of rectangles and triangles (7MS7)
• Calculate areas of compound shapes (e.g. consisting of rectangles and triangles) and volumes
of solids (e.g. cubes and cuboids) (8MS6)
Key Features
• Answers must include units – mm2, cm2 or m2.
• Pupils need to ensure all measurements used are in the same units.
Common Misconceptions
• Errors in basic mental multiplication
• Using the wrong values, in particular not using the perpendicular height when finding
the area of a triangle.
• Multiplying all the values shown.
Examples
1. Calculate the area of the following shapes
9cm
Area = 9 x 3 = 27cm2
3cm
Pupils will
need to identify
the length and
perpendicular
height
2.
6cm
6cm
4cm
8cm
Area of Compound Shapes & Volume
Area = ½ x 8 x 4
= ½ x 32
= 16cm2
Key Teaching Point
To calculate the area of a compound shape pupils will need to split into rectangles or
triangles, find the separate areas and add up to find the total area.
The volume is the amount of 3-dimensional space an object occupies. The formula for the
volume of a cube or cuboid is given below.
Volume = length x width x height
height
width
length
Strand
Using Measuring Skills
Element
Area and volume
Learners are able to
• Calculate areas of compound shapes (e.g. consisting of rectangles and triangles) and volumes
of solids (e.g. cubes and cuboids) (8MS6)
Key Features
• Area is measured in mm2, cm2 or m2.
• Volume is measured in mm3, cm3 or m3.
• Pupils need to ensure all measurements used are in the same units.
Common Misconceptions
• Errors in basic mental multiplication
• When finding the area of compound shapes pupils could easily use the wrong
measurements.
Examples
1.
Calculate the area of the following shape.
Split the overall shape
into two separate
shapes. Shape A is a
rectangle and B is a
triangle.
6cm
4cm
A
7cm
Area of A = 6 x 4 = 24cm2
Area of B = ½ x 6 x 3
= ½ x 18 = 9cm2
Total Area = 24 + 9 = 33cm2
B
Shape B is a triangle with a base of 6cm
and a height of 3cm (because 7 – 4 = 3)
2. Calculate the volume of this cuboid.
Volume = length x width x height
= 7x4x5
= 140cm3
5cm
4cm
7cm
Circles
Key Teaching Point
The area of a circle is found by using the following formulae.
Area of a circle = 𝜋𝑟 2
r
OR
Area of a circle = 𝜋 x r x r
(where r is the radius of a circle, the distance from the centre to the outside and 𝜋 is the
value 3.14)
Strand
Using Measuring Skills
Element
Area and volume
Learners are able to
• Find areas of circles (9MS4)
Key Features
• Area is measured in mm2, cm2 or m2.
• Squaring is the same as multiplying by itself e.g. 32 = 3 x 3 = 9
• Pupils can use 3.14 for 𝜋 or use the 𝜋 button on their scientific calculator.
Common Misconceptions
• Errors in basic mental multiplication
• Using the diameter instead of the radius.
When the diameter
is given – half it to
find the radius
Examples
Find the areas of the following circles
1.
2.
4cm
Area = 𝜋𝑟 2 = 𝜋(42)
= 3.14 x 4 x 4
= 50.24cm2
6cm
Diameter = 6cm therefore Radius = 3cm
Area = 𝜋𝑟 2 = 𝜋(32) = 3.14 x 3 x 3
= 28.26cm2