11.4 More Practice

Extra Questions

A. A solid is a pentagonal prism. Count its faces, vertices and edges, and confirm Euler’s formula.

B. The Koch Snowflake starts from a triangle of side length 5 units. What is its perimeter at Stage 1 and Stage 2?

A. For a prism on an n-gon, F = n+2, V = 2n, E = 3n. With n = 5: F = 7, V = 10, E = 15. Check Euler: F + V = 7 + 10 = 17 and E + 2 = 15 + 2 = 17. They match, so the formula holds.

B. The starting perimeter is 3 \times 5 = 15 units, and each stage multiplies by \tfrac{4}{3}. Stage 1: 15 \times \tfrac{4}{3} = 20 units. Stage 2: 20 \times \tfrac{4}{3} = \tfrac{80}{3} \approx 26.67 units.