A turbine blade with a cooling air flow path specifically directed toward cooling the platform portion of the blade root. Cooling air passages are formed in the blade root platform just below its radially outward facing surface on an overhanging portion of the platform opposite the convex surface of the blade airfoil. Each of these passage extends radially outward from an inlet that receives a flow of cooling air, and then extends through the platform. Cavities are formed in a radially inward facing surface of an over hanging portion of the platform opposite the concave surface of the blade airfoil. An impingement plate directs cooling air as jets into these cavities. A passage is connected to the cavities and directs this cooling air through the overhanging portion of the platform opposite the concave surface.