1.

E is the mid point of medain AD of ∆ABC.(see the given figure)Show that ar(DEC)=1/4ar(ABC)​

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Answer:

ANSWER

Let ABC be a triangle and AD is the median of ΔABC

E is the mid POINT of AD

To PROVE : ar(BED)=

4

1

.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)=

4

1

ar(ABC)

Hence it is PROVED.


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