When we have a two-dimensional (2D) shape, we are able to see how much space it takes up (its area) by counting how many unit squares fit inside the shape. We could count each of the unit squares, but using what we know about arrays means we can use multiplication.

In this video, we use arrays to work out the area of our rectangle, as well as see how else we can work out the area.

What about squares?

A square is a special kind of rectangle, so we can use the same method to work out 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.

Worked Examples

Question 1

We are going to find the area of a rectangle by first identifying the length and the width.

Find the length and width of the rectangle.

width = $\editable{}$ units

length = $\editable{}$ units

Find the area of the rectangle by completing this table.

$\text{Area }$Area	$=$=	$\text{length }\times\text{width }$length ×width	$units$ ²
$\text{Area }$Area	$=$=	$\editable{}\times\editable{}$×	$units$ ²	(Fill in the values for the length and width.)
$\text{Area }$Area	$=$=	$\editable{}$	$units$ ²	(Complete the multiplication to find the area.)

Question 2

Find the area of the rectangle shown.

	width = $2$2 $cm$
length = $12$12 $cm$

$\text{Area }$Area	$=$=	$\text{length }\times\text{width }$length ×width	$cm$ ²
$\text{Area }$Area	$=$=	$\editable{}\times\editable{}$×	$cm$ ²	(Fill in the values for the length and width.)
$\text{Area }$Area	$=$=	$\editable{}$	$cm$ ²	(Complete the multiplication to find the area.)

Question 3

Use for formula $\text{Area }=\text{length }\times\text{width }$Area =length ×width to help you complete the table.

Length Width Area

$5$5 $m$ $12$12 $m$ $\editable{}$ $m$ ²

$\editable{}$ $cm$ $8$8 $cm$ $40$40 $cm$ ²

$2$2 $m$ $\editable{}$ $m$ $22$22 $m$ ²

$6$6 $cm$ $8$8 $cm$ $\editable{}$ $cm$ ²

Length	Width	Area
$5$5 $m$	$12$12 $m$	$\editable{}$ $m$ ²
$\editable{}$ $cm$	$8$8 $cm$	$40$40 $cm$ ²
$2$2 $m$	$\editable{}$ $m$	$22$22 $m$ ²
$6$6 $cm$	$8$8 $cm$	$\editable{}$ $cm$ ²

Time to play

Why not play around with this applet to see just how the area of a rectangle can change when the rows and columns change. Watch how the length and width change, and so does the area, or total number of unit squares.

Created with Geogebra

Remember!

When we calculate area, the unit of measurement is squared. If we have sides measured in centimetres (cm), for example, area will be cm².

Outcomes

5.M2.05

Determine, through investigation using a variety of tools (e.g., concrete materials, dynamic geometry software, grid paper) and strategies (e.g., building arrays), the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas [i.e., Area = length x width; Perimeter = (2 x length) + (2 x width)]

5.M2.06

Solve problems requiring the estimation and calculation of perimeters and areas of rectangles

Area of rectangles and squares

Area