Use the area ratios of similar triangles that appear inside parallelograms and trapezoids.
📘 Example ①
In △ABC, DE ∥ BC and AD:DB = 1:2. Find the area ratio of △ADE and trapezoid DBCE.
Answer: AD:AB = 1:3. △ADE:△ABC = 1:9. Area of trapezoid DBCE = 9 - 1 = 8 parts.
△ADE:trapezoid DBCE = 1:8
In △ABC, DE ∥ BC and AD:DB = 1:2. Find the area ratio of △ADE and trapezoid DBCE.
Answer: AD:AB = 1:3. △ADE:△ABC = 1:9. Area of trapezoid DBCE = 9 - 1 = 8 parts.
△ADE:trapezoid DBCE = 1:8
💡 Key Point
- Area of a trapezoid = whole figure - small triangle
- Calculations are easier when using ratios.
Practice Problems
- In △ABC, DE ∥ BC and AD:AB = 1:4. Find the area ratio of △ADE and △ABC.
Answer and Explanation
- Answer: 1:16. Similarity ratio 1:4 → area ratio 1:16.