# Modeling the relationship between dilations and area?

On a rather basic high school level I want my students to understand the relationship between the scale factor of a dilation and the area of the pre-image and image. For instance if a rectangle has a length and width of 2 and 4 then a dilation takes place and the length and width are now 8 and 16. The area's are 8 and 128 respectively. Although the figure was dilated by a scale factor of 4 the area is dilated by 8(4)(4). How can I get students to discover that relationship by disassociating length and area? So far I am using something similar to this applet. I want my students to make that connection with similar figures without simply telling them

https://www.geogebra.org/m/x2TwNzaq

• Start with counting the number of rectangles (16) that make up the dilated rectangle. You can do this with other shapes that are self-similar, such as triangles. Then move on to non-self-similar shapes by decomposing them into unit squares etc. – Chrystomath Mar 20 at 11:26