# 2 Area

You need to be able to calculate area if you ever need to order a carpet, buy tiles for a kitchen or bathroom, or calculate how much paint to buy when redecorating. You will need all of this at home but also in the workplace if you are responsible for the upkeep of a residential home or a hospital ward.

This play area for children is covered with sponge safety squares that are 1 metre square (each side is 1 metre). How many safety squares are covering the play area?

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 play area is 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 play area is:

6 × 3 = 18 square metres

‘Square metres’ can also be written ‘sq m’ or ‘m^{2}’.

**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 hospital bed

Workout the area of the mattress of the hospital bed.

### Method

To find the answer, you need to work out the width multiplied by the length.

- 90 cm × 2 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 × 2 = area = 1.8 square metres

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

## Activity 4: Finding the area

- The garden of a residential care home contains a fish pond. How much plastic sheeting do you need to cover this pond for the winter?
- Each patient in a hospital ward room needs a minimum space of 10 m
^{2}. Workout the maximum number of patient beds that can be placed in the ward room below: - A medical 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?

### Yeast count

Sample area no. | 21 |

Date | 17 October |

Yeast count | 80 |

Sample dimensions | ? cm × ? cm |

Sample area | ? cm^{2} |

Yeast/cm^{2} | ? |

- An area of forestry land has been identified as a potential location for a new hospital. How large is this area of forestry land?

### Answer

The plastic sheeting needs to be:

- 2.5 × 4 = 10 square metres

First you need to work out the area of the ward room:

- 12 × 6 = 72 square metres

If each patient requires a minimum of 10 square metres of space, you need to divide the area of the ward room by 10:

- 72 ÷ 10 = 7.2

Hence the maximum number of patient beds that can be placed in this ward room is 7 (there is more than enough room for 7 beds but not enough for 8).

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/cm

^{2}) 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 cm^{2} |

Yeast/cm^{2} | 8 |

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 residential care home 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?

- 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!’.
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

First you need to calculate the area of the whole wall:

- 4 × 2.5 = 10 m
^{2}

Then you need to calculate the area of the bookcase:

- 2 × 2 = 4 m
^{2}

Then subtract the area of the bookcase from the area of the wall:

- 10 – 4 = 6 m
^{2}

So the area of the wall that needs painting is 6 m

^{2}.- 4 × 2.5 = 10 m
To calculate the non-winning area of the table, first you need to calculate the area of the whole table:

- 1.5 × 2 = 3 m
^{2}

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

- 0.6 × 0.5 = 0.3 m
^{2}

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

- 0.3 × 2 = 0.6 m
^{2}

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

- 3 – 0.6 = 2.4 m
^{2}

So 2.4 m

^{2}of the table is a non-winning area.- 1.5 × 2 = 3 m

## 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.