Everyday maths 1
Everyday maths 1

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Everyday maths 1

2 Area

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?

Described image
Figure 8 Paving slabs

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 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 a rug

How much backing fabric is needed for this rug?

Described image
Figure 9 A 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 square metres

Now try the following activity. Remember to check your answers once you have completed the questions.

Activity 4: Finding the area

  1. How much plastic sheeting do you need to cover this pond for the winter?
    Described image
    Figure 10 A pond
  2. One bag of gravel will cover half a square metre of ground. How many bags do you need to cover this driveway?
    Described image
    Figure 11 A driveway
  3. 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?
    Described image
    Figure 12 A petri dish

Yeast count

Sample area no. 21
Date 17 October
Yeast count 80
Sample dimensions ? cm × ? cm
Sample area ? cm2
Yeast/cm2 ?
  1. How large is this area of forestry land?
    Described image
    Figure 13 A forest

Answer

  1. The plastic sheeting needs to be:

    • 2.5 × 4 = 10 square metres
  2. 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
  3. 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:

Yeast count

Sample area no. 21
Date 17 October
Yeast count 80
Sample dimensions 2.5 cm × 4 cm
Sample area 10 cm2
Yeast/cm2 8
  1. The area of forestry land is:

    • 4.5 × 2 = 9 square miles

Activity 5: Finding the area of an irregular shape

  1. 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.
    Described image
    Figure 14 A wall

    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?

  2. A charity holds a fundraising fête. A volunteer from the charity designs a game that is played by rolling coins across a table. She marks out two areas labelled ‘WIN!’.
    Described image
    Figure 15 ‘Roll a coin!’

    Anyone who rolls a coin into an area labelled ‘WIN!’ will win a prize. But what is the area of the rest of the table?

Answer

  1. 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.

  2. To calculate the non-winning area of the table, first you need to calculate the area of the whole table:

    • 1.5 × 2 = 3 m2

    Then calculate the area of the ‘WIN!’ areas. One of these is:

    • 0.6 × 0.5 = 0.3 m2

    There are two ‘WIN!’ areas, so you need to multiply this by 2:

    • 0.3 × 2 = 0.6 m2

    You then subtract the ‘WIN!’ areas from the complete area of the table:

    • 3 – 0.6 = 2.4 m2

    So 2.4 m2 of the table is a non-winning area.

Summary

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.

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