Find the shaded area

Geometry Level 4

\(\angle A = \angle ACB = \angle ABC\),
\(GJ = JF \),
\(DI =IF \),
\(HC=CF=FB=BE \),
\(GH = DE = 8\text{ cm} \),
\(AC = 12\text{ cm} \),
\(\text{area}(JCF) = \dfrac14 \text{area}(GHF) \),
\(\text{area}(IBF) = \dfrac14\text{area}(DEF) \).

Find the shaded area up to 3 decimal places.

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