For the hyperbola a2x2−b2y2=1, point P(10,215) gives a2100−b260=1.
The latus rectum length a2b2=8 gives b2=4a.
Substituting: a2100−a15=1, which yields a2+15a−100=0, so a=5 and b2=20.
Thus c2=45 and c=35.
The foci are S(±35,0).
Triangle PSS′ has base SS′=65 and height 215.
Area =21⋅65⋅215=303.
Therefore (Area)2=2700.