Let \(ABCD\) be a square of side length 12.

- \(E\) is the midpoint of \(CB\),
- \( FC = \frac{1}{3} DC \),
- \( GD = \frac{1}{4} DA \),
- \( AH = \frac{1}{3} AE \),
- \(J\) is the midpoint of \(FE\).

What is the area of the purple triangle?

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