Question

in a triangle ABC, E is the mid point of median AD. Show that ar(BED) = 1/4ar(ABC)

Answer 1

AD is the median of ΔABC. Therefore, it will divide ΔABC into two triangles of equal areas. ∴ Area (ΔABD) = Area (ΔACD) ⇒ ... (1) In ΔABD, E is the mid-point of AD. Therefore, BE is the median. ∴ Area (ΔBED) = Area (ΔABE) ⇒ Area (ΔBED) = Area (ΔABD) ⇒ Area (ΔBED) = Area (ΔABC) [From equation (1)] ⇒ Area (ΔBED) =