IKMC 2017 - Grades 7-8 - Self-study Question 30

Question 30

The diagram shows parallelogram ABCD with area S. The intersection point of its diagonals is O. Point M is marked on DC. AM and BD intersect at E; BM and AC intersect at F. The sum of the areas of triangles AED and BFC is $\frac13S$. What is the area of quadrilateral EOFM, in terms of S?

Question illustration

$\frac16S$
$\frac18S$
$\frac1{10}S$
$\frac1{12}S$
$\frac1{14}S$