Many times, small boxes take up too much room to be used effectively. To solve this problem, it might help to build an irregularly shaped box, such as a trapezoidal shape. For example, if you had more room at the back of the shelf but needed to have access to areas near the front, you could build a small box with a wide back, angled sides, and a narrower front panel. Best of all, building one does not require any knowledge of geometry or calculation for the angles involved.
Design a Wooden Trapezoid Box
Mark the 1/8" plywood with your shape. Measure 3 inches in along one long edge and make a small mark. Measure 3 inches in from the opposite corner of the same side and make another mark.
Turn the piece so that your marks are on the side farthest away from you. Place the ruler in a line across the top-left mark and the bottom-left corner. Draw a line between those two points. Repeat the process on the right side of the plywood. Cut the plywood at the lines, removing the corners.
Measure half an inch from one edge of the oak board. Mark a line all the way along the length of the board. Set the circular saw to a blade depth of 1/8th of an inch. Cut along the line, with the blade between the line and the edge of the board.
Place the cut plywood over the piece of oak so that the long side lays on top and one corner of it lines up with one end of the oak board. Mark the board on both sides of the plywood. Miter cut both lines with the saw blade "outside" the line, or on the side between the line and the end of the board.
Flip the plywood back to front so that the shorter of the two longer edges is lined up on the board as you did for the longer piece. Mark the oak board as before. Make the two cuts.
Turn the plywood so that one of the two equal sides is over the oak board. Scribe the ends of the piece and miter cut the angle. Repeat this process for the final side section.
Place the cut plywood on top of the uncut piece. Outline the top piece onto the bottom. Make the cuts "inside" the lines this time, so that the saw blade is positioned between two lines, or edges of the piece you are keeping. This piece will fit inside the groove in the oak sides.
Assemble a Wooden Trapezoid Box
Space two finish nails equally at each end of the two matching boards. Position the nails so that they will drive directly through the angle face of the adjoining boards without shearing out through the side.
Put a thin line of wood glue along the face of all angled cuts. Assemble the pieces, with the bottom panel fitting snugly into the groove as each piece is added. Drive the finish nails in only enough to hold the parts together while the glue dries. Tap them in lightly to avoid jarring other parts loose.
Allow at least eight hours for the glue to bond. Remove the nails. Rub the putty stick over the nail holes to fill them. Sand the surface lightly. Round the corners slightly to prevent chipping.
Measure in 3 inches along the the back side of the box, from the respective corners. Pencil in a small mark. Attach the hinges on the inside of the box with the outside edge of the hinge on the marks you just made. Insert the final hinge screws to attach the lid.
If the bottom panel does not quite fit the grooves, sand the bottom edge of the panel on all sides until it fits snugly.
Stain the top and sides of the box and finish with three or more coats of a high gloss lacquer or varnish.
Cut two pieces the size of the top and position the groove farther up the board to create a "hidden" compartment beneath the visible top box.