Question

in a triangle ABC , e is the midpoint of median ad show that. area b e d = 1\4 area of abc​

Answer 1

hlo mate

here is your answer

In tri.ABC

ABD=ACD-------------(1)

In tri. abd,BE is the median

Abe=bed-------------(2)

now,

ABD=BED

=2(BED)-----------(3)

ABC=ABD+ACD

ABC=2(ABD)-----using(1)

ABC=2*2(BED)----using(3)

ABC=4(BED)

so, (BED)=1/4(ABC)

mark as brainliest

Answer 2

$\huge{\underline{\bf\orange{Answer :-}}}$

Given:

E is the median of AD.

To find:

$ar(BED) = \frac{1}{4} ar(ABC)$

Solution:

Ad is the median of ∆ABC , it will divide ∆ABC into two Triangles of equal area.

∴ ar(∆ABD) =ar(∆ABC)

In ΔABC,

ar(ABD)=ar(ACD) ___________ (1)

In ΔABD, BE is the median

ar(ABE)=ar(BED) __________ (2)

Now, ar(ABD)=ar(BED)

= 2. ar (BED) ______ (3)

ar(ABC)=ar(ABD)+ar(ACD)

ar(ABD)=2.ar(ABD) using (1)

ar(ABC)=2.2.ar(BED) - (2)

ar(ABC)= 4.ar (BED)

∴ar(BED)= 1/4ar(ABC)

Hence it is proved.