Areas and Volumes (for Similar and non-similar figures)


(1) AREAs for Similar Figures

If figures are similar, the ratios of the lengths, widths and even perimeters are the same.
[Note: ratio can be seen as "scale factor".]


[Picture]
http://www.nctm.org/standards/content.aspx?id=26770
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(a) Use the applet to show that the ratios of the lengths, widths and even perimeters are the same


(b) Is the ratio of the LENGTHs the same as ratio of the AREAs?

i) Are the 2 ratios related?

ii) Do we need to find the actual areas (of both the figures) in order to find the ratio?





(2) AREAs and VOLUMEs for Similar Figures


Now that we know that (l1/l2)^2 = A1/A2

Is there any relationship between the (a)ratio of the lengths and (b)ratio of the Areas with ratio of the Volumes?




[Picture]
http://www.nctm.org/standards/content.aspx?id=25097
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