Area and perimeterThe 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

6 cm

3 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 piece of thread.

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 shapesFinding the area of a rectangle is easy if you know the length and width:

4 cm

4 cm

Area = 4 x 4 cm = 16 cm2

5 cm

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 2 cm

Area of big rectangle is 4 x 2 = 8 cm2

Area of square is 2 x 2 cm = 4 cm2

Total area = 12 cm2

Find the area of each shape

3 cm

5 cm

4 cm

4 cm

3 cm

2 cm

2 cm 6 cm

2 cm

3 cm

1. = ___cm2 2. = ___cm2

3. = ___cm2

MeasuresEquivalent 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”

Length

12 inches = 1 foot

2.5 cm

30 cm

3 feet

1 inch

1 foot

1 metre

Mass

16 ounces = 1 pound (lb)25 g

2.25 lb

1 ounce

1 kgCapacity

8 pints = 1 gallon1.75

pints

4.5 litres

1 litre

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 a shape made from unit cubes

Volume = 5 cm3

Volume = 8 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

1 m

20 cm

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