Fix the mistake: Area Ratios
Area Ratios ① Similarity Ratios and Area Ratios (The Secret of Squaring)
For similar figures, the ratio of their areas is obtained by multiplying the ratio of their side lengths by itself. This is an important rule.
🔑 Rule for Similarity Ratios and Area Ratios
Similarity ratio m : n → Area ratio m² : n² (multiply each by itself)
Similarity ratio m : n → Area ratio m² : n² (multiply each by itself)
Example 1: There are two triangles with a similarity ratio of 3 : 5. Find the ratio of their areas.
Solution: 3² : 5² = 9 : 25
Solution: 3² : 5² = 9 : 25
Example 2: The area of the smaller triangle is 18 cm², and the similarity ratio is 2 : 3. What is the area of the larger triangle?
Solution:
① Area ratio is 2² : 3² = 4 : 9
② Proportion → 4 : 9 = 18 : x
③ x = 18 × 9 ÷ 4 = 40.5 cm²
Solution:
① Area ratio is 2² : 3² = 4 : 9
② Proportion → 4 : 9 = 18 : x
③ x = 18 × 9 ÷ 4 = 40.5 cm²
The ratio of volumes is obtained by multiplying the ratio of side lengths three times (m³ : n³). Remember: “area is multiplied twice, and volume is multiplied three times.”
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