`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: AD is a median of `triangleABC`

`therefore` ar(`triangleABD`)=ar(`triangleADC`)=`1/2`ar(`triangleABC`)______1

`therefore` Median of a triangle divides it into two triangles of equal area = 1/2 ar(`triangleABC`)

Again,

BE is a median of `triangle`ABD

ar(`triangleBEA`)=ar(`triangleBED`)=`1/2`ar(`triangleABD`)

(Median of a triangle divides it into two triangles of equal area)

`1/2`ar(`triangleABD`)=`1/2xx1/2`xxar(`triangleABC`) ( from 1)

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