Maths / Areas Of Parallelograms And Triangles / Median and Altitude of Triangle

QUESTION
 

In the given figure, AD is the median of large Delta ACD,;BE is the median large Delta ABD;and;AO is the median of large Delta ABE.

Show that large ar( AOB)=frac {1}{8}ar(ABC). 

EXPLANATION
Explain TypeExplanation Content
Text

AD is a median.

therefore : : : : : : : : : : : ar(Delta ABD)=ar(ADC)

Also, BE is a median

therefore : : : : : : : : : : : ar(Delta ABO)=ar(AEO)

Also, AD is a median.

therefore : : : : : : : : : : : ar(Delta ABO)=ar(ADC)

Now,

ar(ABC)=ar(ABD)+ar(ADC)

=2(ar(ABD))

=2(ar(ABE)+ar(BED))

=2(2ar(ABE))

=2(ar(ABO)+ar(AOE))

=4(2ar(ABO))

       ar(ABC)=8ar(ABD)

Rightarrow         ar(AOB)=frac {1}{8}ar(ABC).

Hence proved

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