In a ` A B C ,\ D ,\ E ,\ F` are the mi-points of sides `B C ,\ C A\ a n d\ A B` respectively. If `a r( A B C)=16 c m^2,` then `a r\ (t r a p e z i u m\ F B C E)=` `4\ c m^2` (b) `8\ c m^2` (c) `12 c m^2` (d) `10 c m^2`

Explanation

Area (`triangleABC`)=`16 cm^2`

Area(trap.`FBCE`)= `triangleABC-triangleAFE`

`1/4`area(`triangleABC`)=area(`triangleAFE`)

area(`triangleAFE`)=`1/4xx16`=`4 cm^2`

NOW, area of trapezium=`16-4`=
`12cm^2`

Hence, option (c) is correct.