What is a Trapezium?

What's in this wiki?

> What is a trapezium?

> Properties of a trapezium at a glance

> Types of trapeziums

> How do I know if it's a trapezium?

> Trapezium or trapezoid?

> How do I find the perimeter and area of a trapezium?

> Trapeziums in real life

> See also

> Resources

What is a trapezium?

A trapezium is a 2D shape that is also known as a trapezoid. To make sure what you’re looking at is a trapezium shape, here’s what it should look like:

For it to be a trapezium it needs to have 4 sides. Two of these slides need to be parallel, but they don’t have to be the same length.

The other sides have to be at different angles and not parallel. If the shape you're looking at matches these criteria then it’s a trapezium.

Properties of a trapezium at a glance

Trapeziums have:

• four sides with only one pair of them being parallel;
• four vertices;
• interior angles that add up to 360°.

What are the trapezium angles?

A trapezium is a two-dimensional shape that falls into the quadrilateral family of shapes. As you read above, it has multiple properties like many other 2D shapes, including angles. All trapezium angles (just as in other quadrilateral shapes) add up to 360°. This means that all four angles within a trapezium will add up to this amount, and won’t exceed it.

Out of the four angles, the two that are adjacent to one another are supplementary; this means that they’ll add to 180° (both are 90°). The other two angles will amount to 180°, but they won’t be the same.

What are the different types of trapezium?

There are three types of trapezium, that have the same names as different types of triangles:

• Isosceles trapezium: This is when the parallel lines of the shape are the same length. It often looks like an isosceles triangle without a pointed top.

• Right trapezium: At least one side of this type of trapezium needs to have two right angles.
• Scalene trapezium: This type doesn’t have equal sides or equal angles. This is the same as a scalene triangle.

How do I know if it’s a trapezium?

Here’s some easy hints as to whether your shape is a trapezium or not. Use these to identify the shapes you’re looking at:

• If both pairs of sides are equal then the shape you’re trying to identify isn’t a trapezium. You’re looking at a parallelogram. It should look like a rectangle that’s been pushed over a little.
• If all the sides are equal in length, parallel and there are four right angles, then you’re looking at a square.
• Much like with squares, if the opposite sides are parallel and equal then it may be a rectangle. Just be sure to measure the sides as a rectangle will have two parallel sides longer than the other two.

Trapezium or Trapezoid?

When you’re researching trapeziums, you might come across the word ‘trapezoid’. This isn’t a problem, but it can be confusing sometimes.

‘Trapezoid’ is the term used in the United States and trapezium is what’s used in the United Kingdom. So, if you ever see these two words you don’t need to worry, they’re the same shape.

How do I find the perimeter and area of a trapezium?

There is a knack to working out the area of a trapezium, and we’re here to let you in on that secret!

Well, it’s really not much of a secret; more like an equation. It goes like this.

To find the perimeter of a trapezium, you need to find the sum of the lengths of its four sides.

To find the area of a trapezium, you have to use the following formula:

In this formula, the big ‘A’ stands for ‘area’. The small ‘a’ represents one of the parallel sides of the trapezium, while the small ‘b’ represents the other. The value ‘h’ stands for the distance between these parallel sides.

When you have these measurements, you essentially have to add together the parallel sides, divide them by two, and then multiply them by the distance between them. Still with us?

For example, on this trapezium, you would first identify and measure the parallel sides. Let’s say that the side measuring 4cm is ‘a’, and the side measuring 8cm is ‘b’. Add these up to get 12cm, and then divide by two to get 6cm. Now, hold onto that number! We’ll be needing it.

Now you need to measure the distance between the parallel sides, which, in this case, is 5cm. From there, simply multiply 6cm by 5cm, which is 30. So, the area of this trapezium is 30cm!

For a few examples on how to find the areas of different shaped trapeziums, take a look at this Area of a Trapezium Wiki Page. It's an in depth guide which is easy to follow. The equation above might look a bit complicated, but this guide will take you through it. There's some examples too, so you can see how it's done.

Where can I find trapeziums in real life?

Here’s a list of places you might find trapeziums in real life. Take a look around the next time you’re out and about, or even in your own home, to see if you can spot any:

• Roofs: If you step outside your house and look at the roof, there’s a big chance that your roof is shaped like a trapezium. If you’re drawing a house, it’s most likely you’re going to draw the roof like that too.
• Bags: Lots of handbags are designed to be in the shape of trapeziums. The larger longer bottom and shorter top make storing things inside easier and safer.
• Bridges: The next time you’re crossing a bridge, take a second to imagine it from the side. Lots of bridges are built with a trapezium shape in mind.
• Cinema: When you’re next going to watch a film at the cinema, take a look at your popcorn bucket. It’s shaped like a trapezium too, I bet you never noticed!
• Home: You can find lots of trapezium-shaped things inside your home, even things you might not have thought of before. Lamp shades are a good example of this, they’re round but if you look at them carefully and imagine they’re 2D you’ll spot it.

Resources to teach trapezium angles:

Here at Twinkl, we have a wonderful range of resources you can use to assist in teaching this topic. You’ll find PowerPoints, worksheets, lesson packs and even display resources – all of which are available to make your life easier! Our maths resources have all been created by a wonderful team of fully qualified teachers who know the curriculum inside and out. With this, you can trust that our materials have been made alongside the national curriculum aims and objectives, which will help you stay on track.

What’s more, our content is accurate, relevant, and up to date. So, no need to waste your time fact checking! Many of our resources also come equipped with answers to adult guidance to help you plan the best lesson for your young learners. What more could you want?

Although children will begin to learn about trapezium angles and how to work out the area of a trapezium in later stages, our resources give a good insight into trapeziums and other quadrilaterals. You can use them as introductory resources and help your young learners develop accurate knowledge and understanding of quadrilaterals shapes.

We have plenty of teacher-made resources for teaching children more about this primary shape - all of which are designed with the Australian curriculum in mind. Take a look at what we have to offer:

Types of Quadrilateral Poster - This is a lovely resource that your children can use as a reference for trapeziums and other shapes. Either keep it small, or print onto A3 paper so that you can include it in a bold display on posters.

2D Shape Properties Display Photos - Similarly, these posters are great for making a colourful display that ensures the properties of different shapes, such as the trapezium, stay at your children’s fingertips.

Maths Area of a Trapezium Worksheet - Try something a little more challenging with this worksheet, which both contains instructions for finding the area of this irregular shape, and questions to solidify the teaching.

See also

• If your little one wants to learn more about shapes, this Properties of 2D Shapes Homework Help page can help.
• Find out more about the properties of different quadrilateral shapes with this Quadrilateral Shape Teaching Wiki.
• Young learners might struggle to remember the difference between a parallelogram and a trapezium, so this teaching wiki on parallelograms can help. Simply read through it and compare the properties of these shapes.