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Areas of Parallelograms and Triangles
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15/07/2021 1:10 pm
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In a triangle ABC, E is the mid-point of median AD. Show that ar(BED) = \(\frac{1}{4}\) ar(ABC).
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15/07/2021 1:13 pm
ar(BED) = (\(\frac{1}{2}\)) × BD × DE
Since, E is the mid-point of AD,
AE = DE
Since, AD is the median on side BC of triangle ABC,
BD = DC
DE = (\(\frac{1}{2}\)) AD — (i)
BD = (\(\frac{1}{2}\))BC — (ii)
From (i) and (ii), we get,
ar(BED) = (\(\frac{1}{2}\)) × (\(\frac{1}{2}\))BC × (1/2)AD
⇒ ar(BED) = (\(\frac{1}{2}\)) × (\(\frac{1}{2}\))ar(ABC)
⇒ ar(BED) = \(\frac{1}{4}\) ar(ABC)