<Qua-2024-724>, hint

1. <APS=<ASP=90-A/2, similarly <BPQ=90-B/2, <DRS=90-D/2, <CRQ=90-C/2

Hence <QPS=(A+B)/2 <QRS=<C+D)/2 <QPS+<QRS=(A+B+C+D)/2=180

Hence P,Q,R,S are concyclic

2, Triangles ABC and ADC are congruent, AC=6 DA=DC=5 Hence Altitude from D to A 

is 4. [ABC] =(4x3)/2=6.. [DSR]=3/5 x 3/5 x6=[BPQ]

[APS]=[BPQ]=2/5 x 2/5x6. [PQRS]=12-2(6x4/25+6x9/25)=144/25