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 is covered with 18 squares that are 1 metre by 1 metre, the area is 18 square metres.
(If you count the squares in Figure 8 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 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 ‘m2’.
Hint: Always use the same units for both sides. If you need to, convert one side to the same units as the other side.
Example: The area of plastic sheeting needed to cover some furniture
How much plastic sheeting is needed to protect this area from paint spillages?
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 square metres
Now try the following activity. Remember to check your answers once you have completed the questions.
Activity 4: 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 the biologist found 80 yeast. What would go in the missing spaces in her recording sheet, as marked with a question mark?
|Sample area no.||21|
|Sample dimensions||? cm × ? cm|
|Sample area||? cm2|
- How large is this area of forestry land?
The plastic sheeting needs to be:
- 2.5 × 4 = 10 square metres
First you need to work out the area of the driveway:
- 8 × 4 = 32 square metres
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 square centimetres
There are 80 yeast, so the amount of yeast per square centimetre (yeast/cm2) is:
- 80 ÷ 10 = 8 yeast per square centimetre
The recording sheet should look like this:
|Sample area no.||21|
|Sample dimensions||2.5 cm × 4 cm|
|Sample area||10 cm2|
The area of forestry land is:
- 4.5 × 2 = 9 square miles
Activity 5: Finding the area of an irregular shape
- The estates manager of a college decides to repaint one of the walls in the reception area. The diagram below shows the dimensions of the wall that needs painting.
The wall is 4 m long and 2.5 m high and has a large fixed bookcase in the corner. What is the area of the section of the wall that needs painting?
You have been asked to paint a wall for a customer. You need to calculate the area of wall that will need emulsion.
What is the area of the wall that needs to be painted with emulsion? Remember you will not be painting the windows.
First you need to calculate the area of the whole wall:
- 4 × 2.5 = 10 m2
Then you need to calculate the area of the bookcase:
- 2 × 2 = 4 m2
Then subtract the area of the bookcase from the area of the wall:
- 10 – 4 = 6 m2
So the area of the wall that needs painting is 6 m2.
To calculate the area of the wall that needs emulsion, first you need to calculate the area of the whole wall:
- 1.5 × 2 = 3 m2
Then calculate the area of the windows. One of these is:
- 0.6 × 0.5 = 0.3 m2
There are two windows, so you need to multiply this by 2:
- 0.3 × 2 = 0.6 m2
You then subtract the window areas from the complete area of the wall:
- 3 – 0.6 = 2.4 m2
So 2.4 m2 of the the wall needs to be painted.
In this section you have learned how to work out the area of a rectangular shape. You have also looked at more complex, compound shapes for calculating area.