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Area of a Trapezium

Check that you can find the area of a trapezium and use the trapezium area formula for problem solving.

Level 1 Level 2 Description Help More Areas

This is level 2: apply the trapezium area formula in different ways. You can earn a trophy if you get at least 7 questions correct and you do this activity online. The diagrams are not drawn to scale.

Trapezium Diagram 1

The area of the trapezium shown in the diagram is 25cm2. Find the value of a

Working:

cm Correct Wrong
Trapezium Diagram 2

The area of the trapezium shown in the diagram is 110cm2. Find the value of b

Working:

cm Correct Wrong
Trapezium Diagram 3

The area of the trapezium shown in the diagram is 475m2. Find the value of c in metres

Working:

m Correct Wrong
Trapezium Diagram 4

Find the area of the trapezium shown in the diagram if its perimeter is 68cm and its height is 20cm

Working:

cm2 Correct Wrong
Trapezium Diagram 5

The area of the composite shape made with two identical trapezia is 3600mm2. Calculate the distance from A to B.

Working:

mm Correct Wrong
Trapezium Diagram 6

Four congruent trapezia are drawn on an empty car park as shown. The total area of the composite shape they form is 2820m2. Find the value of d

Working:

m Correct Wrong
Trapezium Diagram 7

The perpendicular distance between the parallel sides of this trapezium is 14cm. The area of the trapezium is 210cm2. Find the value of x

Working:

cm Correct Wrong
Trapezium Diagram 8

The perpendicular distance between the parallel sides of this trapezium is 13cm. The area of the trapezium is 195cm2. Find the value of y

Working:

cm Correct Wrong




The parallel sides of a trapezium are 8cm apart. The ratio of the lengths of the parallel sides is 6:7. If the area of the trapezium is 364cm2 find the difference between the lengths of the two parallel sides.

Working:

cm Correct Wrong




The parallel sides of a trapezium are 27cm apart. One of the two parallel sides is 10cm longer than the other. If the area of the trapezium is 1107cm2 find the length of the longer of the two parallel sides.

Working:

cm Correct Wrong
Check

This is Area of a Trapezium level 2. You can also try:
Level 1 Areas of other shapes

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Mathematical Salad Blog, Cambridge Maths

Wednesday, October 4, 2017

"What is the definition of a trapezium? Is it a shape with exactly one pair of parallel sides or at least one pair of parallel sides? Or maybe even none at all! Different cultures define a trapezium slightly differently and many have the term trapezoid too. In the US (for some) a trapezium is a four sided polygon with no parallel sides; in the UK a trapezium is a four sided polygon with exactly one pair of parallel sides; whereas in Canada a trapezoid has an inclusive definition in that it’s a four sided-polygon with at least one pair of parallel sides - hence parallelograms are special trapezoids.

To read the full blog post go to Cambridge Mathematics."

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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Description of Levels

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Level 1 - Find the areas of the trapezia

Level 2 - Apply the trapezium area formula in different ways

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Formula

Formula for the area of a trapezium

The area of a trapezium is half the sum of the parallel sides multiplied by the distance between them.

Example

This video is from Mathscasts.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

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