South is perpendicular to West, so the plane's route forms a right triangle, and you can use Good Old Pythagoras to calculate the length of the hypotenuse.
The length of the displacement is √(the west piece² + the south piece²) .
That's √ [ (340km)² + (360km)² ]
= √ [ (115,600) km² + (129,600) km² ]
= √ 245,200 km²
= 495 km
To be technical, Displacement is a vector, so we would need to
calculate its direction too.
Naturally, the plane winds up roughly southwest of where it took off.
You'd want to find the angle whose tangent is (360/340) = about 1.059 .
The direction of the Displacement is that angle south of west. (about 46.6 degrees)