The Purple Triangle of Jeffrey and Trevor

Geometry Level 2

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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