Properties of Polyhedra

This video tutorial by Pedro Ítalo introduces Euler's formula, which relates the number of vertices, faces, and edges in a convex polyhedron. The video explains different types of polyhedra, such as prisms and pyramids, and demonstrates how to use Euler's formula to calculate these elements. Through examples and exercises, viewers learn to apply the formula to various polyhedra, including complex ones like dodecahedrons. The tutorial concludes with practical exercises to reinforce understanding.

What is the relationship between vertices, faces, and edges in a convex polyhedron?

• Vertices + Faces = Edges + 2

• Vertices + Edges = Faces - 2

• Vertices + Edges = Faces + 2

• Vertices + Faces = Edges - 2

What is a convex polyhedron?

• A polyhedron with all faces being concave

• A polyhedron with at least one face being concave

• A polyhedron with all vertices pointing outward

• A polyhedron with all vertices pointing inward

How many vertices does a square-based prism have?

• 8

• 6

• 12

• 10

How many faces does a tetrahedron have?

• 4

• 6

• 5

• 3

What is the formula to find the number of edges if the number of faces and vertices are known?

• Vertices - Faces - 2

• Vertices + Faces + 2

• Vertices + Faces - 2

• Vertices - Faces + 2

How many edges does a dodecahedron have?

• 24

• 36

• 30

• 20

How many faces does a polyhedron with 8 hexagonal faces and 6 square faces have?

• 14

• 12

• 16

• 18

How many vertices does a polyhedron with 8 hexagonal faces and 6 square faces have?

• 22

• 24

• 20

• 26

How many edges does a polyhedron with 20 hexagonal faces and 12 pentagonal faces have?

• 150

• 120

• 90

• 60

How many meters of thread are needed to sew a football with 20 hexagonal faces and 12 pentagonal faces, if each edge requires 15 cm of thread?

• 60 meters

• 54 meters

• 49.5 meters

• 45 meters