Area and Similar triangles. How to find the ratio of areas from the similarity ratio. All you have to do is...

To find the ratio of the areas of similar triangles, just square the similarity ratio.

The ratio of the perimeters on the other hand equals the similarity ratio.

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

As you can see from our knowledge of the formula of area, the ratio of the areas is ratio of areas

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Related: What are Similar Triangles | Theorems proving Similar Triangles| Right Similar Triangles | Side Splitter Theorem | Angle Bisector Theorem |Area & Similarity

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

Area and Similarity Ratio

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

Answer

Problem on similarity, area and perimeter

Area & Similar Triangles

Ratio of areas of similar triangles

Why area's ratio is the similarity's squared