`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 `triangle B E D=1/4 area of triangleA 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 : `ar( triangleBED)=1/4a r( triangleABC)dot`

Explanation

Given: A `ABC, D`
is the mid-point of `BC` and `E` is the mid-point of the median `A`.
To Prove: `ar(triangleBED)=1/4ar(triangleABC)`
Proof: Since `AD` is the median of `ΔABC`, so it will divide `/_\ABC` into two equal triangles.
`therefore ar(/_\ABD)=ar(/_\ADC)`
Also, `ar(/_\ABD)=1/2ar(/_\ABC)` .....(i)
Now, `In /_\ABD`, `BE` is the median,
Therefore, `BE` will divide `/_\ABD` into two equal triangles.
`ar(/_\BED)=ar(/_\BAE)` and `ar(/_\BED)=1/2ar(/_\ABD)`
`ar(/_\BED)=1/2xx[1/2 ar(/_\ABC)]` (Using equation (i))
`:.ar(/_\BED)=1/4ar(/_\ABC)`
Hecne Proved.