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