Let the side length of a square be x, then BP = xsinθ, AP = xcosθ,
By BP+AP=AB, xsinθ+xcosθ = acosθ, so x = asinθ cosθ 1+sinθ cosθ.
So S2 = X2 = (asinθ cosθ1+sinθ cosθ) 2 (6 points).
(2)S 1S2= 12? (1+sinθ cosθ) 2sinθ cosθ = (1+12sinθ) 2sinθ =1sin2θ+1,(8 points)
Let t=sin2θ, because 0 < θ < π 2,
So 0 < 2θ < π, then t = sin2θ ∈ (0, 1)( 10 point).
So s1S2 =1t+14t+1= g (t), g' (t) =? 1t2+ 14