Area & Similar Triangles

  Why area's ratio is the similarity's squared  

The similarity ratio from triangle #1 to #2 is ½.
We can use the formula for the area of a triangle to find that

Area of Triangle #1 = ½(12 • 4) = 24

Area of Triangle #2 = ½(24 • 8) = 96

 Answer 

Similarity Ratio	Area Ratio
3/1	32/1 9/1
3/4	32 / 42 -> 9 / 16
7/9	49 / 81

Find the similarity ratio, the ratio of the areas, and the ratio of the perimeters.

 Answer 

similarity ratio= ½
ratio of perimeters = ½
ratio of areas = ¼

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Find the similarity ratio, areas' ratio, and perimeters' ratio.

 Answer 

similarity ratio=
ratio of perimeters =
ratio of areas =