Thursday, March 1, 2012

Square Within a Square

Given a square with side length a and two pairs of parallel segments, find the area of the shaded square. You can move point B to change the size of the square or point A to change the size of the inner quadrilateral. 
This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to


  1. Prove that the inner quadrilateral is a square.
  2. Find the relationship between the area of the inner quadrilateral the area of the square. 
Download Applet


  1. Funny, I made the answer to 2 in GeoGebra earlier :)

  2. I have created the same applet 2 years ago here: