Any point `D` is taken in the base `B C` of a triangle `A B C\ a n d\ A D` is produced to `E ,` making `D E` equal to `A Ddot` Show that `a r\ ( B C E)=a r( A B C)`

Explanation

Proof : InΔABE, Side is having BD (As a Median)
Now, ar(ΔBED) = ar(ΔBAD) [Median of a Δ divides it into 2 Δ's of equal areas] ...(1)InΔACE, Side AE is having CD (As Median).

Now, ar(ΔECD) = ar(ΔACD) [Median of a Δ divides it into 2 Δ's of equal areas] ...(2)
adding (1) and (2), we get
ar(ΔBED) + ar(ΔECD)=
ar(ΔBAD) + ar(ΔACD)
⇒ar(ΔBEC) = ar(ΔABC)