Cut and attach 3/4" plywood to the outside of the frame. Keep the top edge of the plywood flush with the top of the frame. Cut and attach the plywood bottom to the inside of the frame.
For the top, cut a piece of plywood 1 inch longer and wider than the plywood-covered frame. Draw a line down the length of this top piece 3-1/4 inches in from the edge. Using a circular saw, rip down this line to separate the top piece.
Attach the 3-1/4" top plywood piece to the top of the doubled-up 2x4 back support, using an 18-gauge finish nailer. This is the section of the top to which the strap hinges will be attached.