4 Area
Area is the amount of space a flat shape takes up. You need to be able to calculate area if you ever need to order a carpet for your house, buy tiles for a kitchen or bathroom, or calculate how much paint to buy when redecorating.
This patio has paving slabs that are 1 metre square (each side is 1 metre). How many paving slabs are there on the patio?
Area is measured in ‘square’ units. This means that the area is shown as the number of squares that would cover the surface. So if a patio covered with 18 squares that are 1 metre by 1 metre, the area is 18 square metres.
(If you count them, you will find there are 18 squares.)
Smaller areas would be measured in square centimetres. Larger areas can be measured in square kilometres or square miles.
You can work out the area of a rectangle, like the patio above, by multiplying the long side by the short side:
width × length = area
The patio is:
6 × 3 = 18 square metres
‘Square metres’ can also be written ‘sq m’ or ‘m^{2}’.
Example: The area of a table
Fran sees a rectangular dining table she likes. It measures 2 m by 1.5 m. What is the area of the table?
Method
To find the area we need to multiply the length of the table by the width:
2 m × 1.5 m = 3 square metres
So the table is 3 m^{2}.
Activity 9: Area of a rectangle
Complete the following table by calculating the missing areas without using a calculator. You will have looked at methods for multiplying whole numbers and decimals [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] in Session 1. Show your answers in correct square units.
Length  Width  Area in square units (centimetres, metres, kilometres) 

80 cm  30 cm  
7 m  4 m  
2.5 km  2 km  
5.5 m  2.4 m 
Answer
Length  Width  Area in square units (centimetres, metres, kilometres) 

80 cm  30 cm  2 400 cm^{2} 
7 m  4 m  28 m^{2} 
2.5 km  2 km  5 km^{2} 
5.5 m  2.4 m  13.2 m^{2} 
Hint: Always use the same units for both sides. Sometimes the length and width of the rectangle will be given in different units. They must be in the same unit before you can calculate area, so you may need to convert one side to the same units as the other side.
Example: The area of a rug
How much backing fabric is needed for this rug?
Method
To find the answer, you need to work out the width multiplied by the length.
 90 cm × 3 m = area
First, you need to convert the width to metres so that both sides are in the same units. 90 cm is the same as 0.9 m, so the calculation is:
 0.9 × 3 = area = 2.7 m^{2}
Now try the following activity. You need to carry out the calculations without a calculator, but you can doublecheck your answers on a calculator if needed. If you need a reminder about how to multiply whole numbers or decimal numbers without a calculator, please look back at Session 1 first.
Remember to check if you need to convert the measurements before calculating the area.
Activity 10: Finding the area
 How much plastic sheeting do you need to cover this pond for the winter?
 One bag of gravel will cover half a square metre of ground. How many bags do you need to cover this driveway?
 A biologist is studying yeast growth. In the sample area shown below in purple the biologist found 80 yeast. What would go in the missing spaces in her recording sheet, as marked with a question mark?
Yeast count
Sample area no.  21 
Date  17 October 
Yeast count  80 
Sample dimensions  ? cm × ? cm 
Sample area  ? cm^{2} 
Yeast/cm^{2}  ? 
 How large is this area of forestry land?
Answer

The plastic sheeting needs to be:
 2.5 × 4 = 10 m^{2}

First you need to work out the area of the driveway:
 8 × 4 = 32 m^{2}
If each bag covers half a square metre, you will need two bags for each square metre:
 32 × 2 = 64 bags

First you need to change the width to centimetres. 25 mm is the same as 2.5 cm. Then you can work out the area:
 2.5 × 4 = 10 cm^{2}
There are 80 yeast, so the amount of yeast per square centimetre (yeast/cm^{2}) is:
 80 ÷ 10 = 8 yeast per cm^{2}
The recording sheet should look like this:
Yeast count
Sample area no.  21 
Date  17 October 
Yeast count  80 
Sample dimensions  2.5 cm × 4 cm 
Sample area  10 cm^{2} 
Yeast/cm^{2}  8 

The area of forestry land is:
 4.5 × 2 = 9 square miles
Summary
In this section you have learned how to work out the area of a rectangular shape.