BD-BDMO 2013 Problem 3

Higher Secondary P3

Let $ABCDEF$ be a regular hexagon with $AB=7$ . $M$ is the midpoint of $DE$ . $AC$ and $BF$ intersect at $P$ , $AC$ and $BM$ intersect at $Q$ , $AM$ and $BF$ intersect at $R$ . Find the value of $[APB]+[BQC]+[ARF]-[PQMR]$ . Here $[X]$ denotes the area of polygon $X$ .