# Perimerer, Area and Volume

```Area and perimeter
The perimeter of a shape is easy to work out. It is just
the distance all the way round the edge. If the shape
has straight sides, add up the lengths of all the sides.
These may be given, or you may need to measure
carefully along each of the sides using a ruler.
5 cm
4 cm
3 cm
6 cm
3 cm + 5 cm + 4 cm + 6 cm = 18 cm
If it has curved sides, a piece of string or
cotton may be useful. Go around the edge of
the shape and then measure the length of the
Finding areas
The area of a shape is the amount of surface that it covers.
These shapes both have an area of 8 squares
Tip: If the
shape has
curved
sides, count
all the
squares that
are bigger
than a half
Areas of rectangles and shapes
Finding the area of a rectangle is easy if you know the
length and width:
4 cm
5 cm
4 cm
Area = 4 x 4 cm = 16 cm2
3 cm
Area = 3 x 5 = 15 cm2
To find the area of a shape that is made up from
different rectangles joined together just find the
area of each part and then add them together.
2 cm
4 cm
Area of big rectangle is 4 x 2 = 8 cm2
2 cm
Area of square is 2 x 2 cm = 4 cm2
Total area = 12 cm2
Find the area of each shape
1. =
___cm2
2. = ___cm2
4 cm
3 cm
4 cm
5 cm
3. = ___cm2
3 cm
2 cm
2 cm
3 cm
2 cm
6 cm
Measures
Equivalent measures
Length, mass (or weight) and capacity are all measured
using different units.
Length
1 centimetre (cm) =
10 millimetres (mm)
1 metre (m) = 100cm
1 kilometre (km) = 1000m
Mass
1 kg (kg) = 1000 grams (g)
1 tonne = 1000 kg
Capacity
1 litre (l) = 1000 millilitres (ml)
1 centilitre (cl) = 10 ml
Imperial measures
In the past, we used imperial measures. We still
sometimes use pints, gallons, pounds, inches and feet,
so it worth knowing these:
Remember that
 means “is approximately equal to”
Mass
16 ounces = 1 pound (lb)
Length
12 inches = 1 foot
25 g
 1 ounce
2.25 lb  1 kg
Capacity
2.5 cm
 1 inch
30 cm
 1 foot
1.75 pints  1 litre
3 feet
 1 metre
4.5 litres  1 gallon
8 pints = 1 gallon
Volume
Volume is a measure of the space taken up by a solid
object and is measured in cubic units such as cm3 or
cubic metres m3
A solid such as a cube or cuboid is three-dimensional
(3D) which means you need three measurements to work
out its volume, length, width and height.
Each of these
diagrams represents
unit cubes
Volume = 8 cm3
Volume = 5 cm3
Remember: 1000 cm3 = 1000 millilitres = 1 litre
Each of these 2 cuboids has the same volume, 6 cm3
And the same dimensions: length 3cm width 2 cm, height 1
cm.
The volume of the first can be found by counting the unit
cubes.
The volume of the second is found using the rule:
Volume of a cuboid = length x width x height
3 x 2 x 1 = 6 cm3
Volume of a cube = length x length x length = length3
This cube has sides of length 2 cm
Its volume is 2 x 2 x 2 = 8 cm3
The most important thing to remember when you are
working out practical examples of volume is that all
measurements must be in the same units.
Example 1:
30cm
20 cm
1m
Ann's window box is a cuboid of length 1 m, width
20 cm and height 30 cm. Work out its volume.
Make all the units in centimetres
1 m = 100 cm, so the volume is 100 x 20 x 30 = 60 000 cm3
Example 2:
Igor is working out how many cubic metres of
concrete he will need for his patio. It will be 2
metres wide and 8 metres long and he needs to
make it 10 cm deep. How much concrete will he
need.
Make all the units metres
10 cm = 0.1 m, so the volume is
8 x 2 x 0.1 = 16 x 0.1 = 1.6 m3
Example 3:
Bonny has made a rectangular garden pond 2 m long and
1 m wide. She wants to fill it to a depth of 30 cm. How
many litres of water will she need?
Make all the units centimetres
200 x 100 x 30 = 600 000 cm3
Remember that 1 litre = 1000 cm3
600 000
 1 000 = 600
She will need 600 litres of water
```