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The area of ABC and OBC triangle is 120 and 24 respectively. BC=16, EF=8. Find out the area of OEAF Quadrilateral.

$EF = \dfrac{1}{2} BC$ so,$EF \parallel BC$

So, $\bigtriangleup AEF = \dfrac{1}{4}\bigtriangleup ABC = 30$

Now, $\bigtriangleup OEF$ is similar to $\bigtriangleup OBC$

So, $\dfrac{\bigtriangleup OEF}{\bigtriangleup OBC} = \dfrac{EF^2}{BC^2} = \dfrac{1}{4}$

$\Rightarrow \bigtriangleup OEF = 6$

SO, area of $OEAF = \bigtriangleup AEF + \bigtriangleup OEF = 30 + 6 = 36$

You can't say EF||BC only to see that EF=BC/2. Because E and F mayn't be the midpoints. Thanks