By the way, s? = 3/4 inch? x

In triangle ABP, it is determined by cosine theorem: (AP? +AB？ -PB？ )/(2*AP*AB)=cosx

So, PB? =4-2√3cosx

In triangle PBQ, cosine theorem: (PQ? +BQ？ -PB？ )/(2BQ*PQ)=cosQ

So cosQ=√3cosx- 1.

So, sin? Q= 1-cos？ Q=2√3cosx-3cos？ x

t？ =( 1/2PQ*PB)？ = 1/4sin？ Q=√3/2cosx-3/4cos？ x

So, s? +T？ =√3/2cosx-3/4cos？ x+3/4sin？ x

=√3/2cosx-3/4cos？ x+3/4-3/4cos？

=3/4-3/2cos？ x+√3/2cosx

(Think of it as a quadratic function)

To sum up: if and only if cosx=√3/6, s? +T？ Take the maximum value. 7/8 at most.