Area ratio of similar triangles
For similar triangles, the ratio of their areas equals the square of the ratio of their corresponding sides.
In one line: Sides scale once, areas scale twice.
Practice This ConceptUnderstand it
Area grows faster than side length. When every side is scaled by the same factor, the area changes by the square of that factor, not by the same factor itself.
Example
Formula and rule
Area ratio of similar triangles = (corresponding side ratio)2.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
- 1If similar triangles have sides in the ratio 3:5, their areas are in the ratio 9:25.
- 2If one area is 36 cm², the other becomes 100 cm² when the smaller triangle matches the 3:5 scale.
Method you can reuse
- 1Write the side ratio.
- 2Square both terms.
- 3Simplify the ratio if needed.
- 4Use it for area comparison.
Sketch it in your answer
Mark matching sides clearly before squaring the ratio.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
How is the area ratio of two similar triangles related to their side ratio?
Think first, then show answerHide answer
Common wrong answer
Using 3:5 as the area ratio directly and ignoring the square relationship.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
For similar triangles, the ratio of their areas equals the square of the ratio of their corresponding sides.
- 2
Add for 2 marks
Example: If the side ratio is 2:3, the area ratio is 4:9.
- 3
Add for 3 marks
Area grows faster than side length.
Practice this concept with focused MCQs
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