Q7 of 62 Page 186

The points D and E are on the sides AB and AC of ΔABC respectively, such that DE || BC. If AB = 3 AD and the area of Δ ABC is 72 cm2, then find the area of the quadrilateral DBCE.


Here,


In ΔADE and ΔABC


∠ADE = ∠ABC by corresponding angles (DE∥BC)


∠DEA = ∠BCA by corresponding angles (DE∥BC)


∴ ΔAED ∼ ΔACB


Similarly,


ΔAGD ∼ ΔAFB (where AF ⊥ BC)


⇒ AF = 3AG (∵ AB = 3AD which is given) ----(1)


Similarly,


⇒ BC = 3×DE ----(2)


{by (1) and (2)}



⇒ Area of ΔABC = 9 × Area of ΔADE


(∵ Area of ΔABC = 72 cm2)


⇒ Area of ΔADE = 8 cm2


⇒ Area of DCEB = Area of ΔABC - Area of ΔADE


⇒ Area of DCEB = 72 – 8 = 64cm2


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