In ∆ ABE D is the mid-point of AE. Therefore, BD is the median. Since median divides a triangle in two triangles of equal area.
• In ∆ ACE, D is the mid-point of AE_________________________
Adding (1) and (2), we get
ar (∆ABD) + ar (∆ACD) = ar (∆EBD) + ar (∆ECD)
I think it's the right answer to your question
BC is the common base for both the triangles.
but this information is not enough.
if AD is produced perpendicularly then AD and DE can be considered as heights and can be proved by the formula 1/2bh.
if E is produced through B or C i e if D coincides with B or C , SSS congruence rule can be used and proved.