Rectangle-Triangle Area Relationship

Consider the rectangle and the triangle below.

1.  What do you observe? What are common properties between the two polygons?
2. Drag point D to change the height of the triangle and drag point A or B to change the length of the base. What do you observe?
3. What can you say about the areas of the two figures? Justify your answer. 
4. Click the Show Areas check box in the applet.  Was your answer in 3 correct? 
5. Drag point E. What is the relationship between the area of the rectangle and the area of a triangle? Explain why this is so. 

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

The applet above demonstrates that the area of a triangle is half the area of a rectangle with the same base and height.

Download GGB file

Parallelogram Area Proof

1. Move H to the rightmost part of the segment.
2. What is the relationship between the area of the parallelogram to the area of the rectangle? Why?

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This applet illustrates that the area of a parallelogram is equal to the product of its base and its altitude.

Download GGB File