IKMC 2018 - Grades 11-12 - Self-study Question 28

Question 28

ABCDEF is a regular hexagon as shown. G is the midpoint of AB. H and I are the intersections of GD and GE with FC, respectively. What is the ratio of the area of triangle GIF to that of trapezium IHDE?

Question illustration

$\frac12$
$\frac13$
$\frac14$
$\frac{\sqrt3}3$
$\frac{\sqrt3}4$