The Disappearing Square

The figure below is made up of different shapes. If the shapes are rearranged, a square unit of area disappears.  How can this be?

The solution to this problem involves understanding of area, slope, distance formula, or Pythagorean theorem. You can therefore use this as a problem solving activity to deepen students’ understanding of these topics. You can use the applet below to explore the puzzle. You may also download the student version of the applet.

  1. Move the slider.
  2. What can you say about the areas of the animated shapes before and after moving the slider?
  3. What can you say about the length of the sides of the shapes before and after moving the slider?
  4. Explain what happened to the area using the Pythagorean Theorem.


This material may be downloaded upon sending a request e-mail to jacq.agimat@gmail.com.

 

Guillermo Bautista

Guillermo Bautista

I am interested in integrating technology in teaching mathematics particularly on the use of GeoGebra. You can contact me at gpbautista1@gmail.com.

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Guillermo Bautista
About Guillermo Bautista 8 Articles
I am interested in integrating technology in teaching mathematics particularly on the use of GeoGebra. You can contact me at gpbautista1@gmail.com.

2 Comments

  1. Hola Guillermo si podras publicar ejercicio o aplicaciones de areas con geo-gebra pero en español gracias

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