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Area Model for 3^2 + 4^2 = 5^2, Pythagorean Theorem

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3D model description

Area Model for 3^2 + 4^2 = 5^2: A Beautiful Relationship to Play with!
This is an area model showing that 3^2 and 4^2 make 5^2. It is, of course, a special case of the Pythagorean Theorem. However, this relationship can be explored without reference to the Pythagorean Theorem. It is just a neat way to play with some simple numbers and their connections. The unit square is 10 mm x 10 mm. The 5-square is the collector for the 3-square and the four (4 x 1 ) pieces of a 4-square.

Pedagogically, it gives children some visual and tangible perspectives on integers and their squares, and, more importantly, how to take apart and reassemble things when doing math, which is a big idea in algebra, I think.

Boardman, Michael. (2000). Proof without words: Pythagorean runs. MAA Mathematics Magazine, vol. 73, No. 1, p. 59.

3D printing settings






.1 to .2mm



3D printer file information

  • 3D design format: STL Folder details Close
    • 345_Four.stl
    • 345_five.stl
    • 345_squared-ALL.stl
    • 345_three.stl

    Learn more about the formats

  • Publication date: 2018/07/27 at 16:00




STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides:


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