Question

E is a mid point on median AD of triangle abc show that ar(DEC=1/4 ar(ABC
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Answer 1

Prove:ar(DEC)=1/4ar(AB

Given : AD is the median and E is the mid point of AD .So, AE=ED and BD=CD

Proof :In triangle ABC and ADC

BD=CD

So , ar(ABC)=2×ar(DEC)

ar(DEC)=1/2ar(ABC)...........eq1

In triangle ADC and DEC

E is the mid point so ,AE=ED

ar(ADC)=2×ar(DEC)

ar(DEC)=1/2ar(ADC)......eq2

From equation 1and 2

ar(DEC)=1/4ar(ABC).