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Step-by-step build — 10 steps. Also available as a print sheet.
Screw the back frame together with 3" screws or 2" pocket hole screws, tapering the legs as shown. Use glue and adjust for square.
Attach the 1/4" plywood to the lower portion of the back frame with 1-1/4" screws and glue.
Wrap the upper portion of the back not covered by plywood with burlap, stapled tight along the bottom edge. Use spray adhesive to glue batting over the burlap, following the adhesive can's instructions for the best bond.
Glue batting pieces to the ends of the back frame with spray adhesive, then trim to fit. Set the finished back assembly aside.
Use spray adhesive to attach the foam pad to one plywood seat panel, then attach batting over the foam on the top, front, and sides. Sew a box cushion slipcover from the drop-cloth fabric — one piece 73" x 31", two pieces 31" x 6", and two pieces 73" x 6". Fit the slipcover over the foam and staple the raw edges to the underside of the plywood, hiding the edges.
Cut and sew fabric strips for the front and side skirt, then staple in place, turning edges under to hide raw seams. Sew the back skirt pieces and fit over the back frame, turning under and stapling to the underside of the legs. Skipping the taper on the back frame makes every cut here square, which simplifies this step considerably.
Build the base from the 2x10 sides and cross members — these carry the structural load, so don't worry about the thinner 2x2 aprons being weak; they only keep the fabric tucked under and give the feet something to screw to. Paint or stain the base.
Screw the storage box to the back assembly, through the 2x10 back boards into the back's cross supports, using 3" screws. Flip over and screw the base to the underside of the sofa with 3" screws. Flip back over and attach the cushion top with hinges, supporting them with a strap so the cushion can't collapse forward.
Attach the sofa feet to the underside of the base.
Sand any exposed wood surfaces and finish.
Sew square box-cushion pillows measuring 36" wide x 4" deep x 18" tall: four pieces of fabric 37" x 19", four pieces 19" x 5", and four pieces 37" x 5" per pillow. Stitch right sides together into a box shape, leaving an opening to insert stuffing, then stuff and hand-stitch the opening closed.