# Smallest Area Possible

Geometry 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.

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