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 four sides. So 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, 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 conditions. As you read above, it has multiple properties like many other 2D shapes, including angles. All trapezium angles (as in different quadrilateral shapes) add to 360°. This means that all four tips within a trapezium will add up to this amount and won’t exceed it.
Out of the four angles, the two adjacent to one another are supplementary; this means 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 are some accessible hints as to whether your shape is a trapezium. 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. Instead, 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 and 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, it may be a rectangle. Just be sure to measure the sides as a rectangle will have two parallel sides longer than the other.
Trapezium or Trapezoid?
When researching trapeziums, you might come across the word ‘trapezoid.’ This isn’t a problem, but it sometimes cannot be obvious.
‘Trapezoid’ is the term used in the United States, and trapezium is 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?
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:
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 top, there’s a big chance that your roof is shaped like a trapezium. If you’re drawing a home, you’ll most likely
- Bags: Many 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 many trapezium-shaped things inside your home, even things you might not have thought of before. Lamp shades are an excellent example of this, they’re round, but if you look at them carefully and imagine they’re 2D, you’ll spot it.
