- A1/2
- B1/4
- C1/3
- D1/8
Step-by-Step Solution
Each side of △DEF is half of a side of △ABC (midpoint theorem), so △DEF ∼ △ABC with ratio . Area ratio .
Answer: B) 1/4
D, E and F are the midpoints of the sides of △ABC (equal parts carry equal tick marks). What fraction of the area of △ABC is the shaded △DEF?
Class 10Triangles (Similarity)Geometry — Similarity
Key idea: Areas of similar triangles
**Theorem**: The ratio of the areas of two similar triangles is equal to the SQUARE of the ratio of their corresponding sides.
If ΔABC ~ ΔDEF with scale factor , then
Area(ABC)/Area(DEF) = .
**Why**: area scales as length × length. If both length and breadth scale by , area scales by .
**Example**: Two similar triangles have corresponding sides in ratio 3:5. Area ratio = 9:25.
**Reverse**: if areas are in ratio 16:25, sides are in ratio 4:5 (square root).
If ΔABC ~ ΔDEF with scale factor , then
Area(ABC)/Area(DEF) = .
**Why**: area scales as length × length. If both length and breadth scale by , area scales by .
**Example**: Two similar triangles have corresponding sides in ratio 3:5. Area ratio = 9:25.
**Reverse**: if areas are in ratio 16:25, sides are in ratio 4:5 (square root).
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