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AD is the median of ∆ABC. Therefore, it will divide ∆ABC into two triangles of equal area.
therefore, Area (∆ABD) = Area(∆ACD)
=> Area (∆ABD) = (1/2) area (∆ABC) _________(1)
In ∆ABD, E is the midpoint of AD.
Therefore, BE is the median.
=> Area(∆BED) = (1/2) Area(∆ABD)
=> Area(∆BED) = (1/2)×(1/2) Area (∆ABC) [From (1)]
=> Area(∆BED) = (1/4) Area(∆ABC)
therefore, Area (∆ABD) = Area(∆ACD)
=> Area (∆ABD) = (1/2) area (∆ABC) _________(1)
In ∆ABD, E is the midpoint of AD.
Therefore, BE is the median.
=> Area(∆BED) = (1/2) Area(∆ABD)
=> Area(∆BED) = (1/2)×(1/2) Area (∆ABC) [From (1)]
=> Area(∆BED) = (1/4) Area(∆ABC)
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