AMO · 2027 · Grades 8-9 · Self-study SET 20 Question 4

In the diagram, $ABCD$ is a square of side 6, and $AHD$ and $BCG$ are equilateral triangles inside it. Points $I$ and $J$ are the intersections shown: $I=AH\cap BG$ and $J=DH\cap CG$. Find the area of rhombus $IGJH$. Choose one option.