Place one 14-inch-by-48-inch section of 3/4-inch plywood on a flat surface. Line the two 48-inch edges with wood glue along the top surface.
Press one 48-by-14-inch section of 1/2-inch plywood along the two top surface glue lines. This will create a U-shaped structure when viewed from either end. Hold the wood sections in place for five minutes, or until the glue hardens.
Apply wood glue to three of the four edges of one 13-by-13-inch square of plywood. Insert one square into each end of the U-shaped structure to enclose the structure and create a bin with four sides and a base. Allow the wood to dry for 10 to 15 minutes.
Drive one 5-inch screw every 6 inches along each glued edge. Be sure to flip over the bin structure and drive one screw every 6 inches along the length to secure the two 14-by-48-inch sides to the base. Flip the structure back over.
Place the remaining 14-by-48-inch sheet of 3/4-inch plywood on a flat surface. Measure in 8 inches from each corner along one 48-inch side, and attach a hinge at each location using hinge screws.
Place the 14-by-48-inch sheet of 3/4-inch plywood on top of the bin's open edge, with the hinges along the outside of the plywood. Fold the hinge backs down to secure them to the bin. Drive one hinge screw through each hole to attach the lid to the bin. The lid will rest over all four sides of the toy box, using them for additional seating support.
Place the 14-inch-by-48-inch cushion on top of the bin. Remove the cushion when you need to access the toy chest.