These ‘trisquares’ are made up of three squares and each has an area of 3 square units.

Can you fit them together to make an enlargement of the shape? What is its area?

Can you fit trisquares together to make enlargements of scale factors 3, 4 and 5? What are their areas?

Is it possible to make enlargements of all sizes by fitting trisquares together?

Squared paper would be useful for working on this challenge.


This problem is adapted from the NRICH task L Triominoes with permission of the University of Cambridge. All rights reserved.


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6 Responses to Trisquares

  1. Cynthia Fries says:

    Could you use this in class when teaching enlargement? Click (underneath the problem) on the link to the nrich site and have a look at the Teachers Notes page first, rather than the solution page. When your learners have tried this problem let other teachers know how you introduced it, what resources you used and if you felt it helped them understand the topic.

  2. toni says:

    CAPS requires that Grade 10 work on similarity this term but similarity also comes up in grade 9.

    A good understanding of scale factors (linear and area) is important to understanding similarity and to understanding trigonometry.

    This is a puzzle that also calls for visualisation of the way pieces fit together. Learners can do this by trial and error as with all good jig-saws. It helps to use squared paper and to cut out lots of tri-squares and to do this practically.

  3. Yoli Nyoka says:

    Grade 10 learners are so excited to learn by doing. This means that they explore a lot and they manipulated the trisquares. I always encourage all learners to work on their own.

  4. tvanvught says:

    i agree. The best way of doing this activity is to allow the learners to cut the shapes out and to fit it. In this way they will learn more, and they will make their own discoveries.

  5. Pele Pele says:

    I think I will use the activity to introduce transformation in my grade 10 learners,it will bring attention to learners and guide towards clear understanding of transformation geometry

  6. toni says:

    It is good to have an extension of the task ready to give to high flyers.

    Your learners can extend this task by colouring 4 tri-squares to make an enlargement by linear scale factor 2 and area scale factor 4 and then colouring 12 more tri-squares to make this into an enlargement by linear scale factor 4 and area scale factor 16.

    They could even go on to larger enlargements.

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