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.Exercises

- Prove that the inner quadrilateral is a square.
- Find the relationship between the area of the inner quadrilateral the area of the square.

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

ReplyDeletehttp://www.geogebra.org/en/upload/files/Norwegian/oisteing/kvadratoppgave.html

I have created the same applet 2 years ago here:

ReplyDeletehttp://geogebracentral.blogspot.com/2010/11/square-problem.html