`A B C` is a triangle in which `D` is the mid-point of `B C` and `E` is the mid-point of `A Ddot` Prove that area of ` B E D=1/4a r e aof A B Cdot` GIVEN : A ` A B C ,D` is the mid-point of `B C` and `E` is the mid-point of the median `A Ddot` TO PROVE : `a r( B E D)=1/4a r( A B C)dot`

Explanation

Proof:
Since `AD` is the median of `ΔABC`, so it will divide `ΔABC` into two equal triangles.
`therefore ar(ΔABD)=ar(ΔADC)`
Also, `ar(ΔABD)=1/2ar(ABC)` .....(i)
Now, `In ΔABD`, `BE` is the median,
Therefore, `BE` will divide `ΔABD` into two equal triangles.
`ar(ΔBED)=ar(ΔBAE)` and `ar(ΔBED)=1/2ar(ΔABD)`
`ar(ΔBED)=1/2×[1/2 ar(ABC)]` (Using equation (i))
`∴ar(ΔBED)=1/4ar(ΔABC)`
Hecne Proved.