Euler's formula
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1. A hexagonal prism has 8 faces and 12 vertices. Use Euler's formula F + V − E = 2 to find how many edges it has.
2. An octagonal prism has 10 faces and 16 vertices. Use Euler's formula F + V − E = 2 to find how many edges it has.
3. An octagonal pyramid has 9 faces and 9 vertices. Use Euler's formula F + V − E = 2 to find how many edges it has.
4. A pentagonal prism has 7 faces and 10 vertices. Use Euler's formula F + V − E = 2 to find how many edges it has.
5. A triangular prism has 5 faces and 6 vertices. Use Euler's formula F + V − E = 2 to find how many edges it has.
Answer key · Euler's formula
1. 18
F + V − E = 2, so E = F + V − 2.
E = 8 + 12 − 2 = 18.
It has 18 edges.
2. 24
F + V − E = 2, so E = F + V − 2.
E = 10 + 16 − 2 = 24.
It has 24 edges.
3. 16
F + V − E = 2, so E = F + V − 2.
E = 9 + 9 − 2 = 16.
It has 16 edges.
4. 15
F + V − E = 2, so E = F + V − 2.
E = 7 + 10 − 2 = 15.
It has 15 edges.
5. 9
F + V − E = 2, so E = F + V − 2.
E = 5 + 6 − 2 = 9.
It has 9 edges.
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