Question

. A farmer has a land in form of trapezium ABCD as shown. He cultivate the area shown
by AAOB and ACOD. Here AB || DC and 2AB = 3DC, find the ratio of areas of AAOB and
ACOD.​

Answer 1

Area of  ΔAOB  / Area of ΔCOD  = 9/4  if 2AB = 3 DC

Step-by-step explanation:

Comparing ΔAOB  & ΔCOD

∠AOB = ∠COD  (opposite angles)

∠BAO = ∠DCO  ( as ∠BAC = ∠DCA Equal  alternate interior angle  as AB ║ DC)

Similarly

∠ABO = ∠CDO

=> ΔAOB  ≈ ΔCOD

Ratio of area of triangle  =  (Ratio of sides of Triangle)²

=> Area of  ΔAOB  / Area of ΔCOD  =  (side of ΔAOB  / Side of ΔCOD)²

=> Area of  ΔAOB  / Area of ΔCOD  =  (AB / CD)²

given 2 AB = 3 CD

=> AB/CD = 3/2

=> Area of  ΔAOB  / Area of ΔCOD  = (3/2)²

=> Area of  ΔAOB  / Area of ΔCOD  = 9/4

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