The Department of Mathematics Education. EMAT 6700 J. Wilson

Similar Figures and Their Areas

by: Scott Burrell and Kimberly Young

Using GSP, we will explore how similar figures and their areas compare. Click Here. Begin your exploration by dragging the verticies of the polygon and observing the ratios.

How is the ratio of a pair of corresponding side lengths related to dilation ratio? Note: the dilatio ratio is AB/CD

Using GSP, measure the area of each polygon. Calculate the ratio of the area of the dialated polygon to the area of the original.

What is the relationship between the side length ratio and the area ratio for the similar polygons?

 

 Side length ratios

 2

3

1

1/2

1/10

a/b
 Area ratios            

Make a Conjecture. Explain how the shape of the graph in your sketch supports your conjecture.

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