Circle gets cozy in triangle

Geometry Level 3

In $$\triangle{\text{ABC}}$$, $$\text{AD}$$, $$\text{BD}$$ and $$\text{CD}$$ are the bisectors of $$\angle{\text{BAC}}$$, $$\angle{\text{ABC}}$$ and $$\angle{\text{ACB}}$$ respectively.
If $$\text{AFDE}$$ is a rectangle such that $$\text{AD} = \text{10 cm}$$ and $$\text{AE} = \text{8 cm}$$, find the area of the circle inscribed in $$\triangle{\text{ABC}}$$.

Round your answer( in $${\text{cm}}^{2}$$) to the nearest integer.

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