Question

In fig. ABCD is a trapezium in which AB | | DC and AB = 2DC. Determine the ratio between the areas of ΔAOB and ΔCOD.

Answer 1

In triangle AOB and COD, we  have 
∠AOB = ∠COD,      ...[Vertically opposite angles]
and ∠OAB = ∠OCD,    ...[Corresponding angles]
So, by AA-criterion of similarly, we have
ΔAOB ∼ ΔCOD
⇒ `"Area (ΔAOB)"/"Area (ΔCOD)" = "AB"^2/"DC"^2`
⇒  `"Area (ΔAOB)"/"Area (ΔCOD)" = (2"DC")^2/("DC")^2`
= `(4)/(1)`
Hence, area (ΔAOB) : area(ΔCOD) = 4 : 1.