Subjects geometry

Hexagonal Prism Nets

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1. **Problem Statement:** Identify which of the given nets (A, B, C, D) are valid nets of a hexagonal prism. 2. **Understanding a Hexagonal Prism:** A hexagonal prism has 8 faces: 2 hexagonal bases and 6 rectangular lateral faces. 3. **Properties of Nets for a Hexagonal Prism:** - The net must include exactly 2 hexagons (the bases). - The net must include exactly 6 rectangles (the lateral faces). - The rectangles must be arranged so that they can fold around the hexagons to form the prism. 4. **Analyzing Each Net:** - **Net A:** Has 6 rectangles in a row and 3 hexagons attached (1 above the first rectangle, 2 above the fourth and sixth rectangles). Since there are 3 hexagons instead of 2, this cannot be a net of a hexagonal prism. - **Net B:** Has 6 rectangles in a row and 3 hexagons attached (above the first, second, and sixth rectangles). Again, 3 hexagons instead of 2, so not a valid net. - **Net C:** Has 5 rectangles arranged in an L shape and 2 hexagons (one below the leftmost rectangle and one above the top right rectangle). Since there are only 5 rectangles instead of 6, this cannot be a net of a hexagonal prism. - **Net D:** Has 6 rectangles arranged in a zigzag pattern and 2 hexagons (one below the second rectangle and one above the last rectangle). This matches the required number of faces and arrangement to fold into a hexagonal prism. 5. **Conclusion:** Only Net D is a valid net of a hexagonal prism. **Final answer:** Net D only.