Thanks to the Wallace-Bolyai-Gerwien Theorem we know that any polygon can be dissected into pieces and rearranged to match any other polygon of the same area.

## Equipment needed

Worksheet printouts and scissors

## Curriculum Topics Covered

Angles and geometry; calculating the areas of shapes; properties of polygons

Thanks to the Wallace-Bolyai-Gerwien Theorem we know that any polygon can be dissected into pieces and rearranged to match any other polygon of the same area.

Wallace-Bolyai-Gerwien dates to the early 1800s. Only in 2007 was it proven that there is a hinged dissection between any two polygons of equal area.

The most famous hinged direction is the triangle to square transformation known as “Dudeney’s Dissection” [geogebra file].

This worksheet is available with all of the measurements, angles and hinges labelled on the triangle, and a separate version without this information. The triangles are also available as images should you wish to print them on anything else!

If you make any resources based on this worksheet and would like to share them, email them to katie@think-maths.co.uk and we’ll make them available here.

And finally, here is an animated gif we stole from the Wikipedia page.