1. A polyhedron has 6 vertices and 9 edges. How many faces does it have? A. 3B. 5C. 7D. 92. A polyhedron has 25 faces and 36 edges. How many vertices does it have? A. 11B. 12C. 13D. 14 3. What is the cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron?A. triangleB. squareC. rectangleD. pentagon 4. What is the cross section formed by a plane that intersects three faces of a cube? A. triangleB. squareC. rectangle D. pentagon

Hello Madoudou!

#1

So 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 + 2

V = 36 - 23

V = 13

The correct answer is option C

#3

The 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.