Question

D is the mid-point of side BC of Δ ABC and E is the mid-point of BD. If O is the mid-point of AE, prove that ar(ΔBOE) = 1/8 ar(Δ ABC)

Answer 1

Answer:

Your answer is in the picture.

Hope this helps.

Answer 2

Given : D is the mid-point of side BC of Δ ABC and E is the mid-point of BD and O is the mid-point of AE.

 

To prove : ar(ΔBOE) = 1/8 ar(Δ ABC)

 

Proof :

Since AD and AE are medians of ∆ABC & ∆ABD .  

[Median divides the triangle into two triangles of equal area]

∴ ar (∆ABD) = ½ ar (∆ABC) ……….(1)

and , ar (∆ABE) = ½ ar (∆ABD)......(2)

OB is a median of ∆ABE.

∴ ar (∆BOE) = ½ ar (∆ABE)......(3)

∴ ar (∆BOE) = ½ ar × [½ ar (∆ABD)]

[From eq 2]

∴ ar (∆BOE) = ¼  ar (∆ABD)

∴ ar (∆BOE) = ¼  ar [(½ ar (∆ABC)]

[From eq 1]

ar (∆BOE) = ⅛ ar (∆ABC)

Hence proved….

 

HOPE THIS ANSWER WILL HELP YOU…..

 

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