Rectangular Relations

'Use what you know to work out what you don't! Can you fit these shapes into the rectangles?' 

This activity tests your spatial awareness and ability to experiment! The area of all 2D shapes can, eventually, be related back to a rectangle, so if you know how to find the area of a rectangle, you can work out how to find the area of any other 2D shape! 

This activity focuses on finding the relationship between trapeziums (trapezoids), parallelograms and the rectangle. Can you fit the two trapeziums into the one rectangle? Can you cut & paste the parallelogram in such a way that it fits perfectly inside the rectangle? 

Once successful, produce a poster, to display in the classroom, explaining how to use a rectangle to find the areas of parallelograms and trapeziums.


Equipment: Scissors, Glue, Blu-Tack, Card or sugar paper to use as backing paper for mounting the display, Colouring crayons/felt tips/highlighters.

Templates: Use this template from the Rectangular Relations google doc (also embedded below) enlarged from A4 to A3 format. Students are allowed to cut, paste, fold, draw as much as they like on these shapes to try and find a solution for fitting them precisely within the rectangle. Obviously, during experimentation, it is common to make mistakes which is why there are three parallelogram/rectangle pairs and two sets of trapezium/trapezoid and rectangle pairs.

 Rectangular Relations

Look at the picture above:

(a) Can you fit the parallelogram into the rectangle?"

(b) Can you fill the whole rectangle using two trapeziums/trapezoids?"

(c) What measurements, from your parallelogram, would you need to know to know the length and width of the rectangle? Mark them clearly on your parallelogram.

(d) What measurements, from the trapeziums, would you need to know, to know the length and width of the rectangle? Mark them clearly on your parallelogram.



  • You can cut and paste, rotate, reflect, fold etc. the parallelograms and trapeziums and fit them inside their corresponding rectangle (you will need two trapeziums to fill a rectangle but only one parallelogram)?
  • How do you work out the area of a rectangle?
  • If you manage to get your quadrilaterals to fit inside the rectangles, can you work out what dimensions on the original parallelogram or trapezium (trapezoid) correspond to (a) the length (b) the width, of the rectangle?
  • Would this method work for all parallelograms and trapeziums or only some? 
  • Produce a poster for display in class showing what dimensions you would need to know/measure to work out the area of a parallelogram and a trapezium.
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