When we have a 2D shape, the amount of space it takes up is the area of that shape. This area is measured by comparing the shape to a square of fixed size. Thus the standard units for area are square units with familiar side lengths.
From smallest to largest the common units used for measuring area are:
Just as with lengths, while we can use any of these units to measure an area, it makes the most sense to use a unit that makes the measurement easy to visualise. To be able to visualise and estimate areas, it can be useful to identify common objects that are about the area of these units. For example:
It is most appropriate to use square metres (m^{2}) to measure the area of:
Your classroom
Australia
A matchbox
An exercise book
Your classroom
Australia
A matchbox
An exercise book
It is most appropriate to use square centimetres (cm^{2}) to measure the area of:
Your street
A school playground
Your pencil case
Japan
Your street
A school playground
Your pencil case
Japan
Sometimes, it might occur that two different units of measurement are appropriate. In that case, you can choose either unit to use.
The area of some leaves, for example, could be measured with either mm^{2} or cm^{2}.
Sometimes we may only want an idea of the area of something, without needing an exact measurement. In such a case there are some techniques we can use to estimate area:
Estimate the area of the artwork above the sofa if the sofa is $1.9$1.9m in length.
$1.7$1.7 m^{2}
$0.01$0.01 m^{2}
$5$5 m^{2}
$0.5$0.5 m^{2}
$1.7$1.7 m^{2}
$0.01$0.01 m^{2}
$5$5 m^{2}
$0.5$0.5 m^{2}
Estimate the area of the curved shape below if each square on the grid has an area of $3$3 mm^{2}.
$111$111 mm^{2}
$72$72 mm^{2}
$26$26 mm^{2}
$48$48 mm^{2}
$111$111 mm^{2}
$72$72 mm^{2}
$26$26 mm^{2}
$48$48 mm^{2}
Which of these objects do you think would have an area of about $1$1m^{2}?
goal area on a football field
lid of a shoe box
coffee table
baking tray
goal area on a football field
lid of a shoe box
coffee table
baking tray
Converting units of area is like converting units of length, but this time we want to know how many smaller square units fit into the larger square unit. The following applet can help visualise and understand this type of conversion. Use the slider to have a look at some different conversions:

To convert units of area, such as from square millimetres (mm^{2}) to square centimetres (cm^{2}), it may help to think of how to convert units of length first. The following video explains how to convert units of area.
The conversion factors between the different area units are:
A simple way to remember these factors is to remember the conversion factors for lengths and square the factor for conversion of units of area. If we know that the conversion from cm to m is divided by $100$100, then to convert from cm^{2} to m^{2} we divide by $100$100^{2}, or divide by $10000$10000.
When converting between units of area:
Length conversions (learn this!):
Convert $29800$29800 cm^{2} to m^{2}.
Think: We are converting from cm^{2} to m^{2}, since we are converting to a larger unit we need to divide. The conversion factor between centimetres and metres is $100$100. So we need to divide by $100$100 squared.
Do:
$29800$29800 cm^{2}  $=$=  $29800\div100\div100$29800÷100÷100 m^{2} 
$=$=  $2.98$2.98 m^{2} 
Select the option that shows $3$3 m^{2} converted into cm^{2}.
$3000$3000 cm^{2}
$300000$300000 cm^{2}
$30000$30000 cm^{2}
$300$300 cm^{2}
$3000$3000 cm^{2}
$300000$300000 cm^{2}
$30000$30000 cm^{2}
$300$300 cm^{2}
Convert $0.56$0.56km^{2} to m^{2}.
Just as with length there are other units of area that were traditionally used and some are still in use today in a few countries or used for particular applications.
For large areas of land such as farms or national parks the unit hectares (ha) is sometimes used. This is actually a metric unit, with $1$1 hectare being equivalent to $10000$10000 m^{2}.
An imperial unit used for large areas of land is acres (ac), which is $\frac{1}{640}$1640 square miles or approximately $0.4$0.4 hectares. The imperial units we encountered in lengths, which were inches, feet, and miles, can all be used to form units for area  square inches (in^{2}), square feet (ft^{2}), and square miles (mi^{2}). If given the conversion factor, we can convert between units that we are less familiar with, such as these imperial units.
A block of land is listed as $2.5$2.5 hectares.
(a) If $1$1 hectare is equivalent to $10000$10000 m^{2}, how many square metres is the land?
Think: When converting unfamiliar units it is a good idea to set up the given equivalence as an equation and then use operations, keeping the equation balanced, to find the required amount.
Do:
$1$1 ha  $=$=  $10000$10000 m^{2}  Write the conversion factor in the form of an equation. 
$2.5$2.5 ha  $=$=  $2.5\times10000$2.5×10000 m^{2}  Multiply both sides by $2.5$2.5. 
$2.5$2.5 ha  $=$=  $25000$25000 m^{2} 
(b) If $1$1 acre is approximately $4000$4000 m^{2}, how many acres is the property?
Think: Again let's set this up as an equation and work step by step to find how many acres $25000$25000 m^{2} is.
Do:
$4000$4000 m^{2}  $=$=  $1$1 acre  Write the conversion factor in the form of an equation. 
$\frac{4000}{4000}$40004000 m^{2} 
$=$=  $\frac{1}{4000}$14000 acres  Find the equivalent of $1$1 m^{2} by dividing both sides by $4000$4000. 
$1$1 m^{2}  $=$=  $0.00025$0.00025 acres  
$25000$25000 m^{2}  $=$=  $25000\times0.00025$25000×0.00025 acres  Multiply both sides by $25000$25000. 
$\therefore25000$∴25000 m^{2}  $=$=  $6.25$6.25 acres 
Express $54800$54800m^{2} in hectares.
A property covers an area of $4.5$4.5 hectares. Given that $1$1 hectare is $10000$10000 m^{2}, determine the following:
The area of the property in m^{2}.
The area of the property in acres, given that $1$1 acre is approximately $4000$4000 m^{2}.
American football is played on a field with an area of $12000$12000 square yards.
Given that $1$1 square yard is approximately $0.836$0.836 m^{2}, determine the area of an American football field in m^{2}.
The MCG oval has an area of $17700$17700 m^{2}. How much smaller (in m^{2}) than the MCG oval is an American football field?
choose and use appropriate metric units of area, their abbreviations and conversions between them
estimate the areas of different shapes
convert between metric units of area and other area units