 # Similarity, Area Ratios and Volume Ratios

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Videos, worksheets, stories and songs to help Grade 8 students learn how to convert between length and area ratios of similar polygons and how to identify if two solids are similar and how to convert 1D ratios to surface area and volume ratios.

Similarity and Area Ratios
Is there any relationship between the ratio of the areas of two similar figures?
If two triangles are similar, then their corresponding sides are proportional. Since sides are a length and lengths are one dimensional, the side ratio will not predict the ratio of the areas. To find the area ratios, raise the side length ratio to the second power. This applies because area is a square or two-dimensional property.
Similarity and Volume Ratios
How are the ratios of the surface area of solids related to their corresponding volumes?
If two solids are similar, then their corresponding sides are all proportional. The ratio of their surface areas is the side ratiosquared and note that the ratios of the areas does not give the actual surface areas. The volume ratio for the two solids is the side length ratio raised to the third power. Again, this is not the solids' volume, only the ratio of the volumes.

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