Question

In Adjoining Figure, In Δ ABC, Seg DE || Side BC , DE

BC

=

2

3

, and A(Δ ABC)=32cm2

then Find

Area (▭ BCED) = ?​

Answer 1

Given : Seg DE || Side BC

BC/DE = 2/3

A(Δ ABC)=32cm2

To Find : Area (▭ BCED) =

Solution:

Seg DE || Side BC

DE/BC  = 2/3

ΔADE ≈ ΔABC   ( AAA)

∵ ∠A = ∠A  common   ∠D = ∠B  and ∠E = ∠C  corresponding angles

ΔADE ≈ ΔABC  

=> area of ΔADE /area of   ΔABC  = (DE/BC)²

=> area of ΔADE /32  = (2/3)²

=> area of ΔADE = 32 ( 4/9)

=> area of ΔADE = 128/9

Area (▭ BCED) =   area of   ΔABC - area of ΔADE

= 32 - 128/9

= (288 - 128)/9

= 160/9

Area (▭ BCED)  = 160/9 cm²

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