 # 9.05 Area

Lesson

Can you  use an array  to help solve a multiplication question?

### Examples

#### Example 1

Which of these number sentences describe the array?

There may be more than one correct answer.

A
16 \times 8 =2
B
8 \times 2 = 16
C
16 \times 2 =8
D
2 \times 8 =16
Worked Solution
Create a strategy

If we multiply the number of rows by the number of columns, we find the total number of squares.

Apply the idea

The number sentences which describe the array are options B and D.

Idea summary

We get the same answer whichever way we look at our array.

## Area of shapes

If we have a two-dimensional shape (2D), we can work out how much space it takes up (the area), by seeing how many unit squares fit inside the shape. In the video, you'll see how we do this, as well as how we can add up parts of unit squares.

### Examples

#### Example 2

Find the area of the shape below.

Worked Solution
Create a strategy

Count the total number of squares.

Apply the idea

There are 5 squares inside the shape.

\text{ Area }= 5 \text{ units}^2

Idea summary

To find the amount of space a shape takes up, we can use a unit square.

## Area of rectangles with arrays

Let's look at how we can use arrays and multiplication to find the area, or how much space is inside, a two-dimensional (2D) shape, by counting how many unit squares fit inside it.

### Examples

#### Example 3

What is the area of the rectangle?

Worked Solution
Create a strategy

Count the number of squares.

Apply the idea

There are 12 squares.

The area of the shape is 12 square units.

Idea summary

We can use arrays and multiplication to find the area of a rectangle by multiplying the number of rows by the number of unit squares in each row.

## Area of rectangles using length and width

In this video, we use arrays to work out the area of our rectangle but start naming the dimensions as length and width.

### Examples

#### Example 4

Find the area of the rectangle shown.

Worked Solution
Create a strategy

The length and width tell us how many unit squares each side is broken up into.

Use the area of a rectangle formula: \text{Area}=\text{Length} \times \text{Width}

Apply the idea

We can see that length is 12 \text{ cm} and the width is 2 \text{ cm}.

Idea summary

We don't need to know the unit of measurement when we use unit squares. We can also add up parts of unit squares, if they are not complete squares.

When we calculate area, the unit of measurement is squared. If we have sides measured in centimetres (cm), for example, area will be \text{cm}^2.

### Outcomes

#### MA3-10MG

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