Subjects geometry

Figure Faces 22524A

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1. **State the problem:** We are given four figures: a triangular pyramid (tetrahedron), a rectangular prism, a cube, and another rectangular prism. We need to determine which statement about all these figures is true. 2. **Analyze each statement:** - A) All the figures have at least 1 rectangular face. - Figure 1 (tetrahedron) has only triangular faces, so this is false. - B) All the figures have at least 1 triangular face. - Figures 2, 3, and 4 are prisms with rectangular or square faces, no triangular faces, so this is false. - C) All the figures are prisms. - Figure 1 is a tetrahedron, which is a pyramid, not a prism, so this is false. - D) All the figures are polygons. - Each figure is a 3D solid made up of polygonal faces (triangles, rectangles, squares). - The faces themselves are polygons, but the figures are solids, not polygons. 3. **Clarify terminology:** - A polygon is a 2D shape with straight sides. - The figures are 3D solids composed of polygonal faces. 4. **Conclusion:** - None of the statements A, B, or C are true for all figures. - Statement D is ambiguous because the figures themselves are solids, not polygons, but their faces are polygons. 5. **Most reasonable answer:** Since the question likely means the faces, statement D is true in the sense that all faces of the figures are polygons. **Final answer:** D) All the figures are polygons (interpreted as all faces are polygons).