Turbine Engine with a Blade Assembly Having Cooling Conduits

A gas turbine engine having a blade assembly with a platform, an airfoil, and a shank. The airfoil has a plurality of cooling conduits, and the shank has a plurality of inlet passages to provide cooling fluid to the cooling conduits in the airfoil. The cooling fluid is vented through a plurality of cooling holes along the trailing edge of the airfoil. The blade assembly has specific geometries that improve durability.