Tangle with triangle

Geometry Level 5

Let \(\Delta ABC\) be a triangle with vertices \(A,~B~\& ~C\) and \(D,~E~\&~F\) be the midpoint of sides \(AB,~BC~\&~CA\) respectively.

If \(\color{purple}{AE~=~2.5}\), \(\color{orange}{CD~=~\sqrt{13}}\) and \(\color{green}{BF~=~\dfrac{\sqrt{73}}{2}}\), and \(P\) be the image(reflection) of point \(A\) about side \(BC\).

Then find the area of the quadrilateral \(\color{red}{ABPC}\)

Note the given picture is not necessarily correct.

Try more of my geometry here.

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