Let $ABCD$ be a trapezoid such that $|AC|=8$, $|BD|=6$, and $AD \parallel BC$. Let $P$ and $S$ be the midpoints of $[AD]$ and $[BC]$, respectively. If $|PS|=5$, find the area of the trapezoid $ABCD$.

$\text{ }$ [asy][asy] unitsize(11); for(int i=0; i<6; ++i) { if(i<5) draw( (i, 0)--(i,5) ); else draw( (i, 0)--(i,2) ); if(i < 3) draw((0,i)--(5,i)); else draw((0,i)--(4,i)); } [/asy][/asy] We are dividing the above figure into parts with shapes: [asy][asy] unitsize(11); draw((0,0)--(0,2)); draw((1,0)--(1,2)); draw((2,1)--(2,2)); draw((0,0)--(1,0)); draw((0,1)--(2,1)); draw((0,2)--(2,2)); [/asy][/asy][asy][asy] unitsize(11); draw((0,0)--(0,2)); draw((1,0)--(1,2)); draw((2,1)--(2,2)); draw((3,1)--(3,2)); draw((0,0)--(1,0)); draw((0,1)--(3,1)); draw((0,2)--(3,2)); [/asy][/asy] After that division, find the number of [asy][asy] unitsize(11); draw((0,0)--(0,2)); draw((1,0)--(1,2)); draw((2,1)--(2,2)); draw((0,0)--(1,0)); draw((0,1)--(2,1)); draw((0,2)--(2,2)); [/asy][/asy] shaped parts.

Find all ordered positive integer pairs of $(m,n)$ such that $2^n-1$ divides $2^m+1$.