Question

AD is a median of the triangle ABC. E is the middle point of AD. Prove that area(triangle BED)=1/2 area(triangle ABC).



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Answer 1

In ΔABC, AD is the median. Hence area of Δ ABD = ΔADC.

Hence,Hence area of ΔABD = half of ΔABC.......(1)

In ΔABD, E is the mid point of AD, the median. Hence area of Δ BED = ΔABE.

Hence area of Δ BED = half of ΔABD...(2)

From eq.(1)and (2) we get

$Area of Δ BED = \frac{1}{4} ABC$

Answer 2

Answer:

In ΔABC, AD is the median. Hence area of Δ ABD = ΔADC.

Hence,Hence area of ΔABD = half of ΔABC...(1)

In ΔABD, E is the mid point of AD, the median. Hence area of Δ BED = ΔABE.

Hence area of Δ BED = half of ΔABD...(2)

From eq.(1)and (2) we get

Area of Δ BED = \frac{1}{4} ABABCArea