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 www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Exercises

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

Rectangle Area

Move the sliders that represent the base and the height of the rectangle. What do you observe?


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1.) What is the relationship between the base and the height of the rectangle to its shape?
2.) What is the relationship between the height, base, and the number of unit squares (area) of the rectangle?
3) What conjecture can you make based on your answers above?