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Find the area of triangle ADE (in sq cm) when DE || BC in triangle ABC, AD = 2 cm, DB = 3 cm and the area of trapezium DBCE is 21 sq cm.

Class 10Basic Proportionality TheoremGeometry — Similarity

A5
B3
C8
D4

Step-by-Step Solution

\frac{A D}{A B} = \frac{2}{5} . \frac{Area ADE}{Area ABC} = (\frac{2}{5})^{2} = \frac{4}{25}

. Let area ADE = 4

k

, area ABC = 25

k

, trapezium =

21 k = 21

, so

k = 1

. Area ADE = 4 sq cm.

Answer: D) 4

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