Pdf de apresentação sobre poliedros 9 ano

Poliedros 9 ano matematica

1. POLIEDROS

2. ELEMENTOS DO POLIEDRO

3. FACES
1
2
3
4
5
6
7
8
9
10
11
12
São as superfícies planas
que constituem o sólido

4. By counting the line segments,
a cube has 12 edges.
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
7
8
9
10
11
12
Correspondem às linhas
resultantes do encontro de duas
faces
ARESTAS

5. 1
2
3
5
67
4
8
VÉRTICES
São os pontos de
encontro das arestas

6. PODEMOS CLASSIFICAR OS
POLIEDROS EM DOIS GRUPOS:

7. FORMULA RELAÇÃO DE EULER
V é o número de vértices
A é o número de arestas, e
F é o número de faces
Para os poliedros, existe outra forma de saber o número de arestas, vértices ou faces
dos sólidos, que é através da fórmula de Euler.
V + F = A + 2

8. Poliedro F V A F + V A + 2
Cubo 6 8 12 6 + 8 = 14 12 + 2 = 14
Pirâmide triangular 4 4 6 4 + 4 = 8 6 + 2 = 8
Prisma de base pentagonal 7 10 15 7 + 10 = 17 15 + 2 = 17
Octaedro regular 8 6 12 8 + 6 = 14 12 + 2 = 14
Podemos utilizar a relação de Euler para determinar ou confirmar valores
desconhecidos de V, F ou A, sempre que o poliedro for convexo.

12. Vertices =
Edges =
Faces =
?
What is the name of the solid?
?
?
TRY THIS!
How many vertices, edges and
faces does the solid have?

13. Vertices =
Edges =
Faces =
0
2
3
ANSWER
Notice that a cylinder has no corners,
which means it has 0 vertex.
The edges of the cylinder are the tops
and bottom lines.
The faces of a cylinder is composed of 1
curved face and the top and bottom faces.
Cylinder

14. polyhedron.
Since a cylinder
has 1 curved surface,
we can say that
it is not a

15. FORMULA RELAÇÃO DE EULER
V é o número de vértices
A é o número de arestas, e
F é o número de faces
Para os poliedros, existe outra forma de saber o número de arestas, vértices ou faces
dos sólidos, que é através da fórmula de Euler.
V + F - A = 2

16. EXAMPLE: EULER’S FORMULA WITH
POLYHEDRONS
A pyramid has 5 vertices
and 8 edges, how many
faces does it have?

17. EXAMPLE: EULER’S FORMULA WITH
POLYHEDRONS
Re-arrange the formula to solve for V.
Substitute the values.
Solve.
Step 1:
Step 2:
Step 3:
The pyramid has 5 vertices!

18. Edges = ?
TRY THIS!
How many edges does the solid have?
5 faces and 6 vertices

19. 5 faces and 6 vertices
A triangular prism has 9 edges.
Re-arrange the formula to solve for E.
Substitute the values.
Solve.
Step 1:
Step 2:
Step 3:
ANSWER

20. RECAP:
Polyhedra
(polyhedron singular)
are solids that does not
have a curved surface.
Properties of Solids Polyhedra Euler’s Formula
Euler’s Formula can be used
to calcualte the vertices, faces
and edges of polyhedra.
where:
V is the number of vertices
E is the number of edges, and
F is the number of faces
Vertex
A corner where
lines meet.
Face
The surface
of the figure.
Edge
A line segment
between two vertices.

21. THINK
ABOUT IT!
Euler’s formula can be used to
calculate for the number of
vertices, edges and faces of
polyhedrons and it doesn’t work for
a non-polyhedron like a cylinder.
Why do you think so?
Share your answer in our next session.

22. Mathspace. "Faces, Edges, and Vertices in
Polyhedra | Secondary Math | UK Secondary
(7-11)" Accessed 22 February 2024,
https://mathspace.co/textbooks/syllabuses/
Syllabus-453/topics/Topic-8405/subtopics
/Subtopic-111199/?activeTab=theory
REFERENCE

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