Smallest Area PossibleGeometry Level 4
For a rectangle \(ABCD\) with coordinates \(A = (0,0), B = (5,0)\), \(C= (5,3) , D = (0,3) \), let \(P\) denote a varable point lying between the rectangle \(ABCD\).
And we define \(d(P,L) \) as the perpendicular distance of point \(P\) from line \(L\). Suppose
\[ d(P,AB) \leq \min\left[d(P,BC), d(P,CD), d(P,AD) \right]. \]
Find the area of the region in which \(P \) lies.