In triangle A B C, D and E are the mid-points of A B and B C, respectively. If area (\triangle B E D)=8 {cm}^{2}, then what is the area (A D E C) ( in {cm}^{2}) ?

SSC CGL 23 Aug 2021 Shift 2 Paper

Question : 62 of 100

Marks: +1, -0

In triangle

A B C, D

and

E

are the mid-points of

A B

and

B C

, respectively. If area

(△ B E D)=8 {cm}^{2}

, then what is the area

(A D E C)

(

{cm}^{2})

Solution:

Given,

ar(△ B E D)=8 {cm}^{2}

ar( {ADEC})=

We know that, mid-point cut the line in

1: 2 .

So,

\;{ar ∆ B D E}/{ar ∆ B A C}=(\;{1}/{2})^{2}=\;{1}/{4}

⇒ ar(△ B A C)=4 × 8=32 {cm}^{2}

[ ∵ ar(△ B D E)=8 {cm}^{2}]

∴ ar(A D E C)=ar(△ A B C)-ar(△ B D E)

=32-8=24 {cm}^{2}

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