12.1 – explore solids. polyhedron: a solid that is bounded by polygons
TRANSCRIPT
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12.1 – Explore Solids
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Polyhedron:
A solid that is bounded by polygons
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Faces:
Polygon on the side of the shape
Ex: Pent ABCDFE
Quad EFKL
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Edges:
Where two polygons meet to form a line
Ex: EF
FK
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Vertex:
Where 3 polygons meet to form a point
Ex: E
K
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Non-Polyhedron:
An edge that isn’t a polygon
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Base: Polygon the solid is named after.
Hexagonal Prism Rectangular Pyramid
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Lateral Faces:
Parallelograms or triangles on the sides of the solid
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Prism:
Polyhedron with two parallel, congruent basesNamed after its base
Triangular Prism Hexagonal Prism
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Pyramid:
Polyhedron with one base and lateral facesNamed after its base.
Rectangular Pyramid Pentagonal Pyramid
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Regular: All of the faces are congruent regular polygons
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Convex: Any two points on its surface can be connected by a segment that lies entirely inside or one the solid
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Concave: A side of the solid goes inward
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Cross Section:
Intersection of a plane and a solid
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Euler’s Theorem:
Faces + Vertices = Edges + 2
F + V = E + 2
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Platonic Solids:
Regular Polyhedra, only 5. Named after how many faces they have
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Regular Tetrahedron: 4 faces
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Cube: 6 faces
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Regular Octahedron: 8 faces
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Regular Dodecahedron: 12 faces
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Regular Icosahedron: 20 faces
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Determine whether the solid is a polyhedron. If it is, name the polyhedron. Explain your reasoning.
No, curved sides
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Determine whether the solid is a polyhedron. If it is, name the polyhedron. Explain your reasoning.
Yes,
Rectangular prism
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Determine whether the solid is a polyhedron. If it is, name the polyhedron. Explain your reasoning.
No, curved sides
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Use Euler’s Theorem to find the value of n.
F + V = E + 2
n + 8 = 12 + 2n + 8 = 14
n = 6
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Use Euler’s Theorem to find the value of n.
F + V = E + 2
5 + 6 = n + 211 = n + 2
9 = n
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Use Euler’s Theorem to find the value of n.
F + V = E + 2
8 + n = 18 + 28 + n = 20
n = 12
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Find the number of faces, vertices, and edges of the polyhedron. Check your answer using Euler’s Theorem.
F + V = E + 2
5 + 6 = 9 + 211 = 11
F =
V =
E =
5
6
9
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Find the number of faces, vertices, and edges of the polyhedron. Check your answer using Euler’s Theorem.
F + V = E + 2
6 + 8 = 12 + 214 = 14
F =
V =
E =
6
8
12
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Find the number of faces, vertices, and edges of the polyhedron. Check your answer using Euler’s Theorem.
F + V = E + 2
6 + 6 = 10 + 212 = 12
F =
V =
E =
6
6
10
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Sketch the polyhedron.
Cube
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Sketch the polyhedron.
Rectangular prism
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Sketch the polyhedron.
Pentagonal pyramid
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Determine if the solid is convex or concave.
convex
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Determine if the solid is convex or concave.
concave
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Determine if the solid is convex or concave.
convex
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Describe the cross section formed by the intersection of the plane and the solid.
pentagon
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Describe the cross section formed by the intersection of the plane and the solid.
circle
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Describe the cross section formed by the intersection of the plane and the solid.
triangle