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Question:

In given figure, E is any point on median AD of a triangle ABC. Show that area(ABE) = area(ACE).

Solution:

Given, AD is a median of triangle ABC. Thus, it will divide triangle ABC into two triangles of equal area.
∴area(ABD) = aear(ACD) — (i)
Also, ED is the median of triangle ABC.
∴area(EBD) = area(ECD) — (ii)
Subtracting (ii) from (i),
area(ABD) − area(EBD) = area(ACD) − area(ECD)
⇒area(ABE) = area(ACE) [hence proved]