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9.05 Area

Lesson

Are you ready?

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

Examples

Example 1

Which of these number sentences describe the array?

The image shows an array with 8 columns and 2 rows.

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
\displaystyle \text{Rows}\displaystyle =\displaystyle 2Count the number of rows
\displaystyle \text{Columns}\displaystyle =\displaystyle 8Count the number of columns
\displaystyle 8 \times 2\displaystyle =\displaystyle 16Multiply the columns by the rows
\displaystyle 2 \times 8\displaystyle =\displaystyle 16Multiply the rows by the columns

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.

An image showing an array with 2 columns and 4 rows. Ask your teacher for more infromation.

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.

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Examples

Example 2

Find the area of the shape below.

The image shows an L shape made up of 5 squares. Ask your teacher for more information.
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.

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Examples

Example 3

What is the area of the rectangle?

A rectangle that has 3 rows of 4 squares inside it.
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.

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Examples

Example 4

Find the area of the rectangle shown.

A rectangle of length 12 centimetres and width 2 centimetres.
Worked Solution
Create a strategy

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

An array with 4 columns of 3 squares.

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}.

\displaystyle \text{Area}\displaystyle =\displaystyle \text{Length} \times \text{Width}Use the formula
\displaystyle =\displaystyle 12 \times 2 Substitute the length and width
\displaystyle =\displaystyle 24 \text{ cm}^2Double 12
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

VCMMG224

Solve problems involving the comparison of lengths and areas using appropriate units.

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