Growing Rectangles

What happens to the area and volume of 2D and 3D shapes when you enlarge them?
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Growing Rectangles printable sheet



Imagine a rectangle with an area of $20$cm$^2$

What could its length and width be? List at least five different combinations.

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Growing Rectangles


If you enlarge each of your rectangles by a scale factor of 2, what would their new dimensions be?

What would their areas be?

What do you notice?

What happens when you enlarge rectangles with different areas by a scale factor of 2?

What if you enlarge them by a scale factor of 3? Or 4? Or 5 ...? Or $k$?

What if $k$ is a fraction?

Explain and justify any conclusions you come to.

Do your conclusions apply to plane shapes other than rectangles?

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Growing Rectangles

 

 

 



Now explore what happens to the surface area and volume of different cuboids when they are enlarged by different scale factors.

 

 

 

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Growing Rectangles
 
Explain and justify your conclusions.

Do your conclusions apply to solids other than cuboids?

This problem is based on an idea suggested by Tabitha Gould.