Example 3 - Area
The diagram shows the layout of a backyard.
Mr Lister wants to cover the backyard in either paving stones or gravel. He has two options.
- He can cover the backyard in 0.5 metre by 0.5 metre paving stones. Each stone costs 拢5.50.
- He can cover the backyard in gravel. Gravel costs 拢21 per metre squared.
Which is the cheaper option and by how much?
1. What do I have to do?
Read the question through twice.
Highlight or underline the important pieces of information in the question.
2. What information do I need?
The highlighted words are the most important ones.
The cost for each option needs to be calculated. The question asks which is the cheaper option and by how much, so there is going to be a subtraction.
3. What information don鈥檛 I need?
It doesn鈥檛 matter who the backyard belongs to.
4. What maths can I do?
Step A
Find the area of Mr Lister鈥檚 backyard by splitting the shape into two rectangles. One way to do this is shown in the diagram:
Find the missing width of the smaller rectangle by finding the difference between the highlighted lengths.
\(5 - 3 = 2\)
Therefore the missing width is 2 m.
Work out the total area by adding the two areas together.
\(21 + 8 = 29 \:\text{m}^2\)
Therefore the total area of Mr Lister鈥檚 backyard is 29 m2.
Step B
Work out the area of each paving stone in option 1:
\(0.5 \times 0.5 = 0.25 \:\text{m}^2\)
Work out how many paving stones Mr Lister needs to cover his backyard by dividing the total area by the area of each paving stone:
\(29 \div 0.25 = 116\) paving stones
Therefore Mr Lister would need 116 paving stones.
Alternatively, spilt the diagram up into 0.5 m x 0.5 m squares to scale.
Step C
Work out the cost of buying 116 paving stones by multiplying by 拢5.50.
\(116 \times 5.50 = \pounds638\)
It would cost Mr Lister 拢638 to cover his backyard in paving stones.
Step D
Work out the cost of covering the backyard in gravel by multiplying the cost of the gravel per square metre by the area of the backyard.
\(21 \times 29 = \pounds609\)
It would cost Mr Lister 拢609 to cover his backyard in gravel.
Step E
It is cheaper to cover the backyard in gravel. Work out by how much by finding the difference between the two costs.
\(638 - 609 = \pounds29\)
Therefore it is cheaper to cover Mr Lister鈥檚 backyard in gravel by 拢29.
5. Is my solution correct?
It is important to check any calculations at the end even if they have been done on a calculator.
Ensure any diagrams are labelled clearly.
6. Have I completed everything?
Ensure it is specified that option 2 is the cheaper option.
Check that the final answer is in pounds and seems reasonable. For example, the answer should not be bigger than either of the two values calculated for the cost.