GCSE Maths: The Area Of A Trapezium
Introduction
In GCSE Maths you need to be able to calculate the area of many shapes and one of them is that of the area of a trapezium.
You may or may not get the formula but the best thing to do is to learn it and if you write it down just a few times it will help you to remember it.
You can get easy questions and you can get some awkward questions. Hopefully this article will show how best to approach questions that involve a trapezium.
The Area Of A Trapezium - What you need to know
First you should know what a trapezium actually looks like. Here is a diagram to show you:
The diagram above shows a trapezium and in order to calculate its areas, it is the average of the opposite parallel sides multiplied by the height.
The formula to calculate the area is: A=\frac{1}{2} h(a+b)
Do be careful not to include any of the slant measurements when doing any calculations. These do not fit in the formula.
Calculating the area of a trapezium
Example 1:
Find the area of a trapezium with parallel sides 5cm and 10cm and a height of 4cm.
Above is a sketch just to show you where the actual lengths are. To find the area simply use the formula and substitute in the values that are given.
\text { Area }=\frac{1}{2}(4)(10+5)=30 \mathrm{~cm}^2
Finding the height given the parallel sides and the area
Example 2:
Find the height of a trapezium given that the parallel sides are 4cm and 16cm and where the area is 45cm²
Solution:
When dealing with questions regarding the topic area, it is not essential that you draw out a diagram all the time. But what is important is that you are aware of the formula and that you are able to use it.
Using the formula that we have and substituting the information that we have into it:
\begin{gathered} 45=\frac{1}{2} h(4+16) \\ 90=20 h \\ h=4.5 \mathrm{~cm} \end{gathered}
Finding a parallel side if given the area and height
Example 3:
Find the shorter parallel side of a trapezium given that the longer side is 6cm, the height is 12cm and the area is 42cm²
Solution:
\begin{aligned} & 42=\frac{1}{2}(12)(6+a) \\ & 84=12(6+a) \\ & 7=6+a \\ & a=1 \end{aligned}Functional Maths Problem
This question is worth 5 marks in total and it is important that you are showing all your work.
Look for any clues in the question to determine what calculations you can make. One is the word “area” so let us calculate the area of the field.
To calculate the area of the field you need to recognise that you have a compound shape which consists of a rectangle and trapezium. As well as this you need to calculate new appropriate lengths as seen below:
The area of the rectangle =45 \times 25=1125 \mathrm{~m}^2
The area of the trapezium = \frac{1}{2} \times 30 \times(60+45)=1575 \mathrm{~m}^2
Total area = 1125 \mathrm{~m}^2+1575 \mathrm{~m}^2=2700 \mathrm{~m}^2
What Next?
You are told that 1kg of seed will cover 50 \mathrm{~m}^2 and since the bags are sold as a bag of 8kg then this will cover 50 \times 8=400 \mathrm{~m}^2 \text {. }
Now we can find the number of bags that are needed:
Number of bags = 2700 \div 400=6.75.
It is important to be careful here with your answer. You cannot buy 6.75 bags. So you need to round up to 7.
Finally you can now workout the cost:
\text { Cost }=7 \times £ 56=£ 392 .Walter only has £380 and so does not have enough money.
Summary
And there you have it. A few different scenarios that you should be able to manage if you keep practising the examples again and have a go at the questions below to help reinforce your knowledge.
The area of a trapezium is relevant to both GCSE Foundation and GCSE Higher papers. On the foundation paper you will more than likely see a question towards the back of the paper and is more than likely to be aimed at those aiming for a grade 5 on the foundation paper.
As a part of our face to face GCSE Maths Revision Courses, questions such as this are looked at and suggestions are given on how to use clues within the question to be able to find all the necessary calculations that are needed to solve the question.
It is important you keep practising area of a trapezium questions and preferably under a timed condition. This can help you to cope better with exam nerves. Whether you are doing Edexcel or AQA exam boards it is always important to show your working especially for area based questions as it can be quite easy to make a mistake.
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