Assuming it's a regular shape. You could 'slice' it into three, keeping parallel to any one of its sides.
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Divide it into 3 equal parts.
No, a diamond is not normally cut into a square shape.
You cannot have a quadrant (a quarter) in a shape that is divided into 9 parts!
The answer depends on the shape of the paper when you start.
One possible way to divide a pentagon into five parts is (assuming this is a convex pentagon) to start by placing a dot directly in the center. Then, draw a 5 lines from that center dot connecting to the 5 points around the edge of the pentagon. You should now have 5 triangles instead of 1 pentagon.