Investigating Area by Folding Paper: Warmup Problem

  1. If you fold a square piece of paper along one of its diagonals, like this:

    [[{"fid":"11","view_mode":"full","type":"media","attributes":{"height":220,"width":220,"alt":"Square with a diagonal dotted line","title":"Square with a diagonal dotted line","class":"media-element file-full"}}]]

    then you get a figure like this:

    [[{"fid":"12","view_mode":"full","type":"media","attributes":{"height":220,"width":220,"style":"width: 220px; height: 220px;","alt":"Right isosceles triangle","title":"Isosceles triangle","class":"media-element file-full"}}]]

    What kind of triangle is this? What is the relationship between the area of this triangle and the area of the original square? Explain how you decided on the relationship.


  2. Where in the square below could you fold in order to construct a rectangle with exactly ½ the area of the square? How do you know your rectangle has exactly ½ the area of the square?