Interpret labelled nets, reason about folding and connect faces to three-dimensional objects.
Example 1
A proposed net for a pyramid with a 4−sided base has 3 triangular side faces. Does it have the correct NUMBER of triangular side faces?
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Answer: No
- A pyramid has one triangular side face for every edge of its base, so this pyramid requires 4 triangles.
- 3 is not 4, so the side-face count is incorrect.
Example 2
A proposed net for a pyramid with a 9−sided base has 11 triangular side faces. Does it have the correct NUMBER of triangular side faces?
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Answer: No
- A pyramid has one triangular side face for every edge of its base, so this pyramid requires 9 triangles.
- 11 is not 9, so the side-face count is incorrect.
Example 3
A right prism has two matching 5−sided bases. Each net needs one rectangle for each base edge. How many rectangles are needed to make 5 complete nets?
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Answer: 25
- One 5−sided base has 5 edges, so each prism net needs 5 rectangles.
- 5 nets need 5×5=25 rectangles.