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## Question

1. A polyhedron has 6 vertices and 9 edges. How many faces does it have? A. 3 B. 5 C. 7 D. 9 2. A polyhedron has 25 faces and 36 edges. How many vertices does it have? A. 11 B. 12 C. 13 D. 14 3. What is the cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron? A. triangle B. square C. rectangle D. pentagon 4. What is the cross section formed by a plane that intersects three faces of a cube? A. triangle B. square C. rectangle D. pentagon

## Answer

Hello Madoudou! #1So we have: F which is the number of faces we are looking for E which are the numbers of edges and V the number of vertices We can use the Euler’s polyhedron formula. Which is: V – E + F = 2 Remember we are solving for F. Thus,F = E – V + 2 F = 9 – 6 + 2 F = 9 – 4 F = 5 The correct answer is option B #2 It is almost the same problem. They just want us to find the vertices. V = E – F + 2 V = 36 – 25 + 2V = 36 – 23 V = 13 The correct answer is option C #3The cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron is a Triangle. The correct answer is option A #4 The cross section formed by a plane that intersects three faces of a cube is a Triangle. The correct answer is option A Let me know if you have any questions about the answers. As always, it is my pleasure to help students like you.

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