how to identify the PA if i know the stream using OSLC API/programatically
One answer
When you got the RDF/XML of the Stream you will find inside this RDF a predicate called http://jazz.net/ns/process#projectArea (process:projectArea)
This contains an Object which contains the URI to the project area
<process:projectAreardf:resource="https://clm.test:9443/rm1/process/project-areas/_E47WgMQbEemTBO1S3Izw6Q"/>
If you query for this URI the server returns an RDF/XML containing the project area data.
<rdf:Descriptionrdf:about="https://clm.test:9443/rm1/process/project-areas/_E47WgMQbEemTBO1S3Izw6Q">
<dcterms:titlerdf:datatype="http://www.w3.org/1999/02/22-rdf-syntax-ns#XMLLiteral">Project Auf RM 1</dcterms:title>
<acc:accessContextrdf:resource="https://clm.test:9443/rm1/acclist#_E47WgMQbEemTBO1S3Izw6Q"/>
<process:isAccessPublicrdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">false</process:isAccessPublic>
<process:isAccessVisibleToMembersrdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</process:isAccessVisibleToMembers>
<oslc:serviceProviderrdf:resource="https://clm.test:9443/rm1/oslc_rm/_E47WgMQbEemTBO1S3Izw6Q/services.xml"/>
<rdf:typerdf:resource="http://jazz.net/ns/process#ProjectArea"/>
<oslc:instanceShaperdf:resource="http://jazz.net/ns/process/shapes/ProjectArea"/>
<process:isAccessVisibleToAccessListrdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">false</process:isAccessVisibleToAccessList>
<dcterms:modifiedrdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2019-08-29T10:55:55.000Z</dcterms:modified>
</rdf:Description>
If you use Eclipse Lyo you can create classes for Stream and also for Project and unmarshall the RDF/XML into them.