 # 8.05 Order and compare areas

Lesson

## Ideas

We can work out the  area of a shape  by seeing how many squares fit inside it. Try this question.

### Examples

#### Example 1

Find the area of the shape by counting the number of grid squares it covers.

Each grid square represents 1 square unit.

Worked Solution
Create a strategy

Count the total number of the shaded squares to find the area.

Apply the idea

\text{Area}=32 \text{ square units}

Idea summary

To find the area of a shape on a grid, we can count the number of unit squares inside the shape.

## Compare the area

When we  compared length  , we looked at which object was shorter, or longer than the other. We used number lines or lines to help us do this. We can do a similar thing with area, but instead of lines, we use squares.

When we compare area, we can use a square unit to do this. So if we are working with centimetres, we use a square measuring 1\text{ cm} \times 1\text{ cm}. We can use the same method if we working with metres, but instead using a 1\text{ m} \times 1\text{ m} square.

In this video, we'll compare some shapes using a 1\,cm unit square.

### Examples

#### Example 2

Look at the two shapes on the grid.

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 shapes.

Idea summary

To compare areas in the same units, we can compare the size of the numbers.

## Compare area of objects

In this video we look at the area of objects in our everyday life, and how we might compare them. Which unit square should we use? What if we were to use a sheet of paper? Let's find out what happens when we do.

### Examples

#### Example 3

Caitlin's vegetable garden is 54 \text{ m}^2. Her flower garden is 27 \text{ m}^2. Which garden is smaller?

Worked Solution
Create a strategy

We can compare the values of the areas in a number line. The smaller the number, the further it will be to the left.

Apply the idea

Plot both numbers on a number line.

Since 27 is further to the left than 54, so 27 \lt 54.

The flower garden is smaller.

Idea summary

We can use number lines to compare the size of areas of every day objects.

## Different units of measurement

If both our values (numbers) and units of measurement are different, we can use what we know about a unit square to help work out which shape might have the largest area.

### Examples

#### Example 4

Which of these is the larger area?

A
40\text{ cm}^2
B
40\text{ m}^2
Worked Solution
Create a strategy

Since the measurements have the same number we need to compare the size of the units.

Apply the idea

1 \text{ m} is equivalent to 100\text{ cm}, so a metre is larger than a centimetre.

Option B: 40\text{ m}^2 is the larger area.

Idea summary

When comparing the area of objects, don't just compare the numbers. Remember to compare the units of measurement as well.

### Outcomes

#### MA2-10MG

measures, records, compares and estimates areas using square centimetres and square metres