1. **Problem Statement:** A sheet of A4 paper (297mm x 210mm) is folded once and then laid flat on the table. We need to determine which of the given shapes could not be made by folding and explain why. 2. **Understanding the problem:** Folding a rectangular sheet once creates a shape that is either a rectangle or a shape that can be formed by folding along a straight line. The resulting shape must be a polygon whose edges are formed by the original edges or the fold line. 3. **Shapes given:** - a) Square - b) Triangle with a horizontal base, vertical right side, and diagonal side rising from left base to top right - c) Vertical rectangle - d) Trapezoid with long horizontal bottom, short horizontal top, vertical right side, and diagonal left side - e) Horizontal rectangle 4. **Key rule:** Folding once means the shape after unfolding is symmetric about the fold line. The fold line acts as a line of symmetry. 5. **Analysis:** - a) Square: Folding a rectangle once can produce a square if folded such that the shorter side matches the longer side partially. Possible. - b) Triangle with described sides: A triangle with one vertical side and one diagonal side rising from the base to the top right cannot be formed by folding once because folding creates shapes symmetric about the fold line, and a triangle with these sides is not symmetric about any fold line from a rectangle. Not possible. - c) Vertical rectangle: Folding once can produce a smaller vertical rectangle. Possible. - d) Trapezoid with described sides: Folding once can produce a trapezoid if the fold line is diagonal or vertical. Possible. - e) Horizontal rectangle: Folding once can produce a smaller horizontal rectangle. Possible. 6. **Conclusion:** The shape that could not be made by folding once is the triangle described in b). **Final answer:** The triangle in option b) could not be made by folding the A4 sheet once.