12.1 Exploring Solids Polyhedron Platonic Solids Cross Section.
12.1– Explore Solids
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Transcript of 12.1– Explore Solids
12.1– Explore Solids
Polyhedron:
A solid that is bounded by polygons
Faces:
Polygon on the side of the shape
Ex: Hex ABCDFE
Quad EFKL
Edges:
Where two polygons meet to form a line
Ex: EF
FK
Vertex:
Where 3 polygons meet to form a point
Ex: E
K
Non-Polyhedron:
An edge that isn’t a polygon
Base: Polygon the solid is named after.
Lateral Faces:
Parallelograms or triangles on the sides of the solid
Prism:
Polyhedron with two parallel, congruent basesNamed after its base
Pyramid:
Polyhedron with one base and lateral facesNamed after its base.
Regular: All of the faces are congruent regular polygons
Convex: Any two points on its surface can be connected by a segment that lies entirely inside or on the solid (rubberband)
Concave: A side of the solid goes inward
Cross Section:
Intersection of a plane and a solid
Euler’s Theorem:
Faces + Vertices = Edges + 2
F + V = E + 2
Platonic Solids:
Regular Polyhedra, only 5. Named after how many faces they have
Regular Tetrahedron: 4 faces
Cube: 6 faces
Regular Octahedron: 8 faces
Regular Dodecahedron: 12 faces
Regular Icosahedron: 20 faces
Determine whether the solid is a polyhedron. If it is, name the polyhedron. Explain your reasoning.
No, curved sides
Determine whether the solid is a polyhedron. If it is, name the polyhedron. Explain your reasoning.
Yes,
Rectangular prism
Determine whether the solid is a polyhedron. If it is, name the polyhedron. Explain your reasoning.
No, curved sides
Use Euler’s Theorem to find the value of n.
F + V = E + 2
n + 8 = 12 + 2n + 8 = 14
n = 6
Use Euler’s Theorem to find the value of n.
F + V = E + 2
5 + 6 = n + 211 = n + 2
9 = n
Use Euler’s Theorem to find the value of n.
F + V = E + 2
8 + n = 18 + 28 + n = 20
n = 12
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
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
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
Sketch the polyhedron.
Cube
Sketch the polyhedron.
Rectangular prism
Sketch the polyhedron.
Pentagonal pyramid
Determine if the solid is convex or concave.
convex
Determine if the solid is convex or concave.
concave
Determine if the solid is convex or concave.
convex
Describe the cross section formed by the intersection of the plane and the solid.
pentagon
Describe the cross section formed by the intersection of the plane and the solid.
circle
Describe the cross section formed by the intersection of the plane and the solid.
triangle
HW Problems
#31
12.1 798-799 3-6, 11-19 odd, 22-24, 31, 32
Ans: D