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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