Topics
7. Measurement
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AustraliaNSW
Stage 3

7.05 Units of area

Lesson
Practice
Lesson

Are you ready?

 Comparing objects with different areas  will help us to estimate in this lesson. Let's try a problem to review.

Examples

Example 1

Look at the two shapes on the grid.

A grid with Shape A which is a square with 9 tiles and Shapes B which is a square with 25 tiles.
a

What are the areas of Shape A and Shape B?

Worked Solution
Create a strategy

Count the number of squares shaded for each shape.

Apply the idea

There are 9 squares in shape A.\text{Area of Shape A}=9\text{ square units}

There are 25 squares in shape B.\text{Area of Shape B}=25\text{ square units}

b

Which is the smallest shape?

Worked Solution
Create a strategy

We can compare the values of areas.

Apply the idea

Since 9 is less than 25, Shape A is the smallest shape.

Idea summary

We can easily compare the area of shapes if their units are the same.

Appropriate units of area

When we have a 2D shape, the amount of space it takes up is the area of that shape. Choosing the appropriate unit of measurement can mean things make more sense, so let's see how to do this in the video.

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Examples

Example 2

It is most appropriate to use square metres \left(\text{m$^2$}\right) to measure the area of:

A
Your classroom
B
An exercise book
C
A matchbox
D
Australia
Worked Solution
Create a strategy

Think about what units would be appropriate to measure each object.

Apply the idea

Square millimetres \left(\text{mm$^2$}\right) is suited for tiny objects, so we could use it to measure the area of a matchbox.

Square centimetres \left(\text{cm$^2$}\right) is suited for smaller objects, so we could use it to measure the area of a matchbox or an exercise book.

Square metres \left(\text{m$^2$}\right) is suited for big sizes, so we could use it to measure the area of your classroom.

Square kilometres \left(\text{km$^2$}\right) is suited for bigger places, so we could use it to measure the area of Australia.

The answer is option A.

Idea summary

We can use some measurements of length from smallest to biggest: \text{mm$^2$}, \text{cm$^2$}, \text{m$^2$}, \text{km$^2$}.

Estimate the area

This video looks at how to use what you know about size and space to estimate area.

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Examples

Example 3

What is the most appropriate estimate for the area of a postage stamp?

A
5 \text{ cm}^2
B
3 \text{ m}^2
C
5 \text{ km}^2
Worked Solution
Create a strategy

Think about the area of things we know and compare it to the given object.

Apply the idea
ObjectArea
\text{Coin}5 \text{ cm}^2
\text{Bed}3 \text{ m}^2
\text{Lake}5 \text{ km}^2

The table shows objects that have areas similar to the three options.

Since a postage stamp has roughly the same size of a coin with an area of 5 \text{ cm}^2, the answer is option A.

Idea summary

Sometimes, it might be that two different units of measurement are appropriate. In that case, you can choose which one to use. The area of some insects, for example, could be measured with \text{mm$^2$} or \text{cm$^2$}.

A good strategy when estimating the area is to think about the area of things we know. This helps us determine if things make sense, or not.

Outcomes

MA3-10MG

selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles

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