Everyday maths for Construction and Engineering 1

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# 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?

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 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?

Figure 9 Plastic sheeting

### 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?
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?
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?
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?
Figure 13 A forest

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.
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. You have been asked to paint a wall for a customer. You need to calculate the area of wall that will need emulsion.

Figure 15 A wall with two windows

What is the area of the wall that needs to be painted with emulsion? Remember you will not be painting the windows.

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 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.

## 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.

FSM_SSC_1

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