7.07 Area of rectangles

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?

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.

Find the 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 2

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.

Find the area of rectangles with 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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A square is a special kind of rectangle, so we can use the same method to work out the area. Instead of having a different number for our length and width, each side has the same length. Markers are often used, rather than write the length on every side, as this picture shows.

Examples

Example 3

Find the area of the rectangle shown.

Worked Solution
Create a strategy

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

The area of a rectangle is given by \text{Area}=\text{Length} \times \text{Width}.

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