This problem was posted and solved in another thread by Fistfiz.
http://www.mathisfunforum.com/viewtopic … 75#p233175
We are given that ABCD is a square and P and Q are midpoints. We need the ratio of BEFG to ABCD.
Let's see what can be done with geogebra.
1) Turn off the xy axes.
2) Use the regular polygon tool to draw the square ABCD. Label it as in the diagram below.
3) Use the midpoint tool to create points P and Q.
4) Use the line segment tool to draw AP,BP,CQ and BQ.
5) Use the intersect tool to create points E, F, and G.
6) Use the polygon tool and click on points B, E, F and G. Poly2 will be created.
7) Go into options and increase rounding to 15 digits.
8) Type in the input bar, n = poly2 / poly1.
9) Immediately in the Algebra pane you will see under the heading Number, n= .266666666666666...
This is the fraction 4 / 15 which you can guess at or take to Alpha.
9) Drag point D up and down to generate as many squares as you like. What do you notice about n? Stays the same, doesn't it? We are done with geogebra.