QQuestionMathematics
QuestionMathematics
# Problem Solving
10. Nanako said she drew a square pyramid and that all of the faces are triangles. Is this possible? Explain.
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the definition of a square pyramid
- A square pyramid has a square base and four triangular lateral faces - The base is a 2D square shape - The lateral faces connect the base vertices to a single point (the apex)
Step 3:: Analyze the number of faces
- A pyramid always has one base and triangular lateral faces - In a square pyramid, the base is a square (which is a polygon) - The lateral faces are triangles that connect the base vertices to the apex
Step 4:: Verify Nanako's statement
- Nanako claims "all faces are triangles" - This is NOT possible for a square pyramid - The base of a square pyramid is a square (a 4 -sided polygon), NOT a triangle
Step 5:: Explain why
- A square pyramid MUST have at least one non-triangular face (the square base) - To have ALL faces be triangles, the base would need to be a triangle - This would make it a triangular pyramid, not a square pyramid
Final Answer
A square pyramid cannot have all faces as triangles because the base must be a square, which is a 4 -sided polygon, not a triangle.
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