How to Make a Square Pyramid Out of Paper
A square pyramid is a simple geometric shape. It has a square base and four identical triangular sides. You can make a paper square pyramid of almost any size you want. The base has to be a perfect square. Then, each side will be identical isosceles triangles. The base of the triangles (joining the square bottom) has to be shorter than the other two sides of the triangle. The longer the top sides of the triangle are, the higher the pyramid will be.
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Instructions
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Draw the square base (any size) on a piece of paper. Place the square in the center of the paper, and leave space on the paper to each of the four sides about the same width and height as the square.
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Set the compass. Using a common geometry compass, set the distance the same length as one side of the square (place the point of the compass on one corner of the square, and the pencil tip on an adjacent corner).
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Mark the triangle apex. Place the tip of the compass exactly on one corner of the square. Trace an arc with the pencil for a short span directly above the center of the flat sides of the square on either side of the corner. Repeat for each of the four corners.
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Mark the triangle sides. The four points where the arcs overlap are the apexes of the triangle sides. Using a ruler, draw a line from the corners to the adjacent apexes. Draw a line from each corner to each adjacent apex--there are two for each corner. You should have a shape that looks like a four-pointed star, with the square in the center, when you are done.
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Add tabs for gluing. If you want to glue your pyramid together, add paper tabs to one side of each of the triangles (either each left hand or each right hand side). Make the tabs trapezoidal, not rectangular--or they won't fit when you put the pyramid together.
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Cut out the pyramid. Use scissors or a knife to cut the outline of the four triangles and tabs. Do not cut the lines around the square--these will be folded.
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Fold the tab on each triangle. Fold them straight up, exactly along the line, against the triangle.
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Fold the sides. At the base of each triangle (the line adjoining the square base), fold each triangle up and inward.
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Glue the sides. Put a light amount of glue on a tab and glue the tab inside the adjoining side. Repeat for each side. The last side is more difficult because you can't get inside the pyramid to press the edges together. Either fold the tab outward a little, so it applies its own pressure when fit inside the last side, or gently press the sides together from the outside.
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Tips & Warnings
You can add a small hole in the bottom and blow inside to reshape a paper pyramid. Use heavier paper if you are going to paint or otherwise finish the pyramid. Set the compass to a greater length for a taller pyramid. Exact angles on different dimension pyramids have to be calculated carefully. Experiment or learn the math using Different Dimensions (See References for link).
