A platform cooling arrangement for a turbine rotor blade having a platform at an interface between an airfoil and a root, the root including attachment means and a shank, wherein the platform comprises a suction side that includes a topside extending from an airfoil base to a suction side slashface, and wherein the platform overhangs a shank cavity. The platform cooling arrangement may include: a pocket formed in an underside region of the platform, the pocket comprising a mouth that fluidly communicates with the shank cavity; a manifold extending from the suction side slashface to a pressure side slashface, the manifold including a connection to the pocket; and cooling apertures that extend from connections made with the pocket and manifold to ports.