Area

The area of a shape is the amount of space inside the shape.

Areas can be found by counting squares or by using a formula.

Finding areas − by counting squares

For the rectangle shown you can count the number of squares.

Area_01.gif

Counting the squares, there are 21 square centimetres (squares with each side of length 1 cm)
Finding areas − by using a formula

Area_03.gif

It can be seen that there are three rows of seven squares so a quicker way to get the area would be to multiply 3 by 7. This method gives an equation or formula, which works for any rectangle:

Area = length × width = 7 × 3 = 21 square centimetres.

Units

The units used for measuring areas depends on the units used for measuring the length of the shape.

If the units of a shape are not given, the area is given as units2.

A square metre is the area occupied by a square with each side 1 metre long. It is written as 1 m2.

Other common units for area are:

Unit
Symbol
Units for measuring:
Square centimetre
cm2
Small shapes
Square kilometres
km2
Area_04.jpg 
Large areas such as the area of countries
Hectare
ha
Land area, e.g. farms
 

Area Formulae Area_Formula.jpg

Shape
Name
Area
Area_05.gif
Square

A = length × width

= l2
Area_06.gif
Rectangle

A = base × height

= b × h

= bh

Converting between units

To convert between units of area is sometimes confusing. A diagram often helps.

Example

Square metres into square centimetres

To convert 1 m2 into cm2.

Multiply by 10 000
Area_07.gif

From the diagram

1 m2 = 100 × 100 cm2 = 10 000 cm2

Hectares into square metres

Convert 1 ha into m2.

Multiply by 10 000
Area_08.gif

From the diagram

1 ha = 100 × 100 m2 = 10 000 m2

 

Composite Shapes

Composite shapes are shapes made up of shapes such as squares, rectangles, semicircles etc.

To find out the area of composite shapes, break the larger shape up into smaller ones for which you can find the area.

Example First method

Find the area of the following composite shape:

Area_09.gif

Break the shape up into two rectangles and find the missing measurements:

Area_10.gif

Area needed = area of A + area of B

= 10 × 5 + 7 × 6 = 92 cm2
Another method Yet another method!

Break the shape up into two other rectangles and find the missing measurements:

Area_11.gif

Area needed = area of C + area of D

= 4 × 5 + 12 × 6 = 92 cm2

Find the area of the bigger rectangle and subtract the un-needed bit.

Area_12.gif

Area needed = area of rectangle − un-needed bit

= 10 × 12 − 7 × 4 = 92 cm2