# Is the information sufficient?

Geometry Level 4

In the diagram, $$AC=1$$, where $$C$$ is the midpoint of side $$AB$$ of triangle $$ABJ$$. Square $$BCDE$$ is drawn, where $$D$$ lies on side $$AJ$$ and $$E$$ is in the interior of the triangle. Square $$FGIH$$ is drawn, where $$G$$ lies on side $$BJ$$, $$H$$ lies on side $$AJ$$, $$I$$ is in the interior of the square, and $$E$$ is the midpoint of $$FG$$.

Find the area of triangle $$ABJ$$.

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