IKMC 2017 - Grades 9-10 - Self-study Question 13

Question 13

From the side midpoints of an equilateral triangle, six perpendiculars to its sides are drawn as shown. What fraction of the original triangle is covered by the resulting shaded hexagon?

Question illustration

$1/3$
$2/5$
$4/9$
$1/2$
$2/3$