Maximum Area

The area of $ABCD$ will be maximum when the area of $\triangle PAB, \triangle PBC, \triangle PCD$ and $\triangle PAD$ will be maximum.

Area of $\triangle PAB = \frac{1}{2} \times h \times PA$ .
$PB=8$ will be the maximum height if the angle between $PA$ and $PB$ is a right angle. So, Maximum area of $\triangle PAB = \frac{1}{2} \times PB \times PA = 16$

It's similar for the other three triangles.

Maximum area of $\triangle PBC = 24$

Maximum area of $\triangle PCD = 15$

Maximum area of $\triangle PAD = 10$

.

Hence, Maximum area of $ABCD = 16 + 24 + 15 + 10 = \boxed{65}$