Wednesday, July 6, 2011

I see parallelograms everywhere

Having come to terms with the area of the triangle - and realising how parallelograms unlock the secrets of so many of our basic regular shapes ....

... it's time to look at our friend the trapezium (or trapezoid if you insist). 

Can you turn this into a parallelogram? And how does it help work out the area?

Try it out, before clicking to see more. A teacher resource is also provided at the end of the post.

This is just too much fun!

Here's a teacher resource for use in class - first page gives no answers, second page gives a strong helping hand. A US version using the word 'trapezoid' instead of 'trapezium' is also provided.
Trapezium Exploration (Australia/British version)

Trapezoid Exploration (US version)


  1. Thanks for sharing. I've never seen it this way before. I will surely use this in my classroom!

  2. Another clear explanation of this concept, and illustration of the formula! Love the graphics.

  3. I selected this to be the lead article in my online paper today: "Teach Better Math Lessons, Today":

  4. Funny thing is - I had never seen it that way either until this morning! A few days ago, a friend showed me the cutting in half trick, but we turned then manipulated the pieces into a rectangle (to get the same effect). This morning I realised we didn't need to the last step - the parallelogram was right there asking to be seen.

  5. I've always explained it by duplicating the trapezium and turning it around to make the parallelolellogram, but this way is more obvious. Good stuff!

  6. Even easier .. draw a diagonal to make two triangles! Area top triangle is 1/2 a x h, area of the bottom triangle is 1/2 b x h - add them together (student must know a little algebra) : 1/2 (a + b ) x h

  7. Thank you for sharing. I have a similar post here:

    You and your readers may want to check it out.