We fold a paper using GeoGebra and explore a problem from American Mathematical Contest (AMC 10)

Problem: A rectangular piece of paper whose length is \( \sqrt 3 \) times the width has area A. The paper is divided into three equal sections along the opposite lengths, and then a dotted line is drawn from the first divider to the second divider on the opposite side as shown. The paper is then folded flat along this dotted line to create a new shape with area B. What is the ratio B: A?

You may also try another paper folding scenario. Here we make the crease a variable!