1. **Problem statement:** A sheet of A4 paper (297mm x 210mm) is folded once and then laid flat. We need to determine which of the given shapes (a square/rectangle, triangle, tall rectangle, trapezoid-like quadrilateral, wide rectangle) could not be formed by a single fold. 2. **Key concept:** Folding a sheet once creates a shape that is the union of two congruent parts, symmetric about the fold line. The resulting shape must be symmetric along the fold line. 3. **Analysis of each shape:** - a) Square/rectangle: Possible by folding along a line parallel to one side. - b) Triangle: Impossible because folding once always produces a shape symmetric about the fold line, and a triangle is not symmetric about any line unless it is isosceles with the fold along the axis of symmetry. Since the original sheet is rectangular, folding once cannot produce a triangle shape. - c) Tall rectangle: Possible by folding along the longer side. - d) Trapezoid-like quadrilateral with one slanted side: Impossible because the fold line symmetry would require the slanted side to be mirrored, producing a symmetric shape, not a trapezoid with only one slanted side. - e) Wide rectangle: Possible by folding along the shorter side. 4. **Conclusion:** Shapes b) triangle and d) trapezoid-like quadrilateral cannot be formed by folding once and laying flat because they lack the required symmetry. **Final answer:** Shapes b) and d) could not be made by folding once.