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