Question

In ∆ABC, E is the mid-point of median AD. Show that ar(BED)=1/4 ar(ABC).​​

Answer 1

Answer:

Given: A ∆ABC in which D is the mid-point of BC and E is the mid-point of AD.  

To prove: ar(∆BED) = 1/4 ar(∆ABC).  

Proof : ∵AD is a median of ∆ABC.  

∴ ar(∆ABD) = ar(∆ADC) = 1/2 ar(∆ABC) .....(i)   [∴Median of a triangle divides it into two triangles of equal area) = 1/2 ar(∆ABC) Again,

∵ BE is a median of ∆ABD,  

∴ ar(∆BEA) = ar(∆BED) = 1/2 ar(∆ABD)   [∴Median of a triangle divides it into two triangles of equal area]  

And 1/2 ar(∆ABD) = 1/2 x 1/2 × ar(∆ABC) [From (i)]

∴ ar(∆BED) = 1/4 ar(∆ABC).

Answer 2

hey mate

here is your answer

ar(∆ ABD)=1/2ar(∆ABC)

ar(∆BDE)=1/2(∆ABD)

ar(∆BDE)=1/2×1/2ar(∆ABC)

ar(∆BDE)=1/4ar(∆ABC)

........hence proved

hope it helps u ...