The Area of an Equilateral Triangle

Rotate the blue triangle and orange and pink quadrilaterals.Then adjust points A, B, C, and D until you form a new Quadrilateral. Show the side lengths. Then compare the area.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Questions:
1. Why is the area of the quadrilateral the same as the area of the original equilateral triangle?

2. What positions for A, B, C, and D make the quadrilateral a square? Why do you think this is?

3. Why do we decompose and compose polygons into other polygons? What is the advantage?

Dixie Christensen, 12 November 2013, Created with GeoGebra