In a ` A B C` if `D\ a n d\ E` are mid-points of `B C\ a n d\ A D` respectively such that `a r\ ( A E C)=4\ c m^2` , then `a r\ ( B E C)=` `4\ c m^2` (b) `6\ c m^2` (c) `8\ c m^2` (d) `12 c m^2`

Explanation

Since AD is the median of `triangleABC`

ar(`triangleABD`)=ar(`triangleADC`)________1

EC is the median of `triangleADC`

ar(`triangleAEC`)=ar(`triangleDEC`)_____2

ar(`triangleDEC`)=`4cm^2`

EC is the median of `triangleBED`

ar(`triangleBED`)=ar(`triangleDEC`)____3

From 2 and 3

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