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In a triangle ABC, E is the mid-point o...

In a triangle `ABC`, `E` is the mid-point of median `AD`. Show that `a r\ (B E D)=1/4a r\ (A B C)```

Text Solution

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We know, the median of a triangle, divides the triangle into two triangles of equal areas.
So, in `Delta ABC`
`ar(ACD)=ar(ABD) = 1/2ar(ABC)->(1)`
Also, we are given,`E` is the mid-point of `AD` that means `BE` is the median of `Delta ABD`
So,
`ar(BED)=ar(AEB) = 1/2ar(ABD)`
From (1),
`ar(BED) = 1/2(1/2ar(ABC))`
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