# 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.

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