AMO 2027 Grades 9-11 SET 3 - Self-study Question 9

In the diagram, $ABCD$ is a square, and $AHD$ and $BCG$ are equilateral triangles. Points $I,J$ are the intersections shown. If the square has side length 6, find the area of rhombus $IGJH$. The source diagram is schematic, not to scale.



Choose one option.