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2019 Math Kangaroo

Problem 5

Problem 5 · 2019 Math Kangaroo Medium
Geometry & Measurement off-by-one

A pyramid has 23 triangular faces. How many edges does this pyramid have?

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Answer: C — 46
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Hint 1 of 2
A pyramid over an n-sided base has n triangular side faces; here every face is a triangle.
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Hint 2 of 2
Match the number of triangular faces to the base size, then count base edges plus slant edges.
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Approach: relate faces and edges of a pyramid
  1. A pyramid over an n-gon base has exactly n triangular side faces.
  2. So 23 triangular faces means the base is a 23-gon.
  3. Such a pyramid has 23 base edges plus 23 slant edges to the apex, total 46 edges.
  4. Answer (C) 46.
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