Question

In a triangle ABC , E is the mid point of median AD . show that ar (BED) = 1/4 ar (ABC)

Answer 1

are(ABC) (ad×BC)/2
ar(bed). (ed×bd)/2 but ed is ad/2. and bd is BC/2
(ad/2×bc/2)/2. =. (ad×bc)/8
ar(ABC)/ar(bed). =(ad×bc/2)/(ad×bc/8)
it gives ar(ABC) =4ar(bed)
hence ur answer
1/4ar(ABC) =ar(bed)
j

Answer 2

Answer:

Given:-

∆ABC in which D is the midpoint of BC and E is the midpoint of AD.

To Prove:-

ar(∆BED) = ¼ ar(∆ABC)

Proof:-

•°•AD is the median of ∆ABC.

•°•ar(∆ABD) = ar(∆ADC) = ½ ar(∆ABC)

[Median of a triangle divides it into two triangles of equal areas.]

•°•AD is the median of ∆ABD.

•°•ar(∆BEA) = ar(∆BED) = ½ ar(∆ABC)

[Median of a triangle divides it into two triangles of equal areas.]

And ½ ar(∆ABD)= ½ × ½ × at(∆ABC)

•°• ar(∆BED) = ¼ ar(∆ABC)//

hope it's helpful ☺️☺️☺️.

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