Cut a groove, follow a curve

in the attached file i want to cut a square groove, red box, to follow the purple curve and end up with a solid.
i can’t get wire cut to follow the line.
is there such a thing as Extrude Cut?
grove.3dm (142.7 KB)

sorry if i jumped the gun, i tried a sweep 1, that gave me an open polysurface, then i cap planer holes and made a solid, then did a boolean difference and that made my groove