BEING UNFAMILIAR WITH THE AREA; A PA28 PLT WAS UNABLE TO UNDERSTAND AND COMPLY WITH TWR INSTRUCTIONS TO REMAIN CLR OF RENTON; WA; AIRSPACE.

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DEPARTING BFI RWY 31R TO DIRECT YAKIMA ON VFR FLT PLAN. INITIAL TWR CTLR BEFORE TKOF ASKED ME FOR R TURN AND THEN TURN ON COURSE VIA 'THE ISLAND' TO STAY CLR OF RENTON; WA; AIRSPACE. SAID I WAS UNFAMILIAR WITH THAT VFR CHKPOINT AND HE EXPLAINED. UPON TKOF; TWR ASKED FOR R DOWNWIND DEP. I EXECUTED THAT; BUT IT DID TAKE ME OVER RENTON TWR-CTLED AIRSPACE WHEN I WAS IN CONTACT ONLY WITH BFI TWR. I TRIED TO CLARIFY; BUT BY THAT TIME I WAS JUST PAST BFI HDG 130 DEGS AND IT WAS TOO LATE. IN RETROSPECT; I LIKELY SHOULD HAVE COMBINED THE TWO: NOT TURNED DOWNWIND UNTIL A COUPLE OF MI XWIND ON A HDG OF ABOUT 040 DEGS. ALTERNATIVELY; THE TWR COULD HAVE CLARIFIED WHERE/WHEN HE WANTED DOWNWIND TURN WHEN HE SPECIFICALLY ASKED FOR THAT. I GENERALLY THINK OF A DOWNWIND DEP AS BEING 'WHEN ALT PERMITS A SAFE TURN TO DOWNWIND;' WHICH IS PRETTY CLOSE-IN WHEN CLBING FROM SEA LEVEL IN THIS ACFT. I THINK WE BOTH COULD HAVE DONE A BETTER JOB OF IT -- THOUGH; FOR THE RECORD; THE RESPONSIBILITY LIES IN THE COCKPIT; IN MY VIEW. (I DID NOT HAVE CURRENT SEA TERMINAL AREA CHART OPEN AND AVAILABLE; AS WELL AS CURRENT SEA SECTIONAL.)