7.07 Area of rectangles

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

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

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

Watch question walkthrough

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 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.

Watch question walkthrough

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

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}.

\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}^2	Double 12

Watch question walkthrough