KöMaL 2011 B4344

The lengths of the parallel sides of a symmetric trapezium are $a$ and $c$. The midpoints of the legs are $E$ and $F$. Let $G$ denote the orthogonal projection of point $E$ on the line of the leg $BC$. What is the area of the trapezium if point $C$ divides the line segment $GF$ in a 1:2 ratio? ($C$ lies closer to point $G$.)