The four coloured pieces can be put together in two different ways to make these shapes with base 13 units and height 5 units. Why is there one square missing in the second arrangement?
Topics: Starter  Area  Mensuration  Puzzles  Ratio  Shape
Here's a classic 'Missing Square' dissection. The pieces don't change area. Where does the square come from? Attributed to Mitsunobu Matsuyama. Interactive @geogebra file here: https://t.co/ffBYXQYFYy pic.twitter.com/ZFLvsxzdda
— Ben Sparks (@SparksMaths) February 27, 2021
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Sam Loyd presented this Chessboard Paradox at the American Chess congress in 1858. Notice the Fibonacci numbers which can be found in both of these diagrams.
As you probably guessed, even though the red lines don't look parallel they actually are.
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Teacher, do your students have access to computers such as tablets, iPads or Laptops? This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments: Transum.org/go/?Start=July26 However it would be better to assign one of the student interactive activities below. 

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The images on this page are from the Wikimedia Commons. The descriptions of the licences can be found on the following pages: Missing Square Puzzle and Sam Lloyd Image.