The above is a GIF showing the mechanism of a very simple but impractical leg. However, in maths, nothing is impractical.

It is known that the red colour circle above is of radius \(1\).

The coordinates of the purple point are \((0,-3)\).

And the length of the black line (or leg) is \(5\).

The green egg-shaped shape traces the path of the bottom of the black leg.

Given that the area of the green egged-shaped shape is \(A\), find \[\left\lfloor 1000A \right\rfloor. \]

To be fair, you may use a computational method.

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