Chapter 11 Surface Area

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Chapter 11 Surface Area Volume
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Sec. 11 1 Space Figures Cross Sections

• Objective
• 1) To recognize polyhedra and their parts.
• 2) To visualize cross sections of space
  figures.

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Polyhedrons

• Polyhedron Solid with all flat surfaces that
  enclose a single region of space.
• 3D Solids or Space Figures (includes circles)
• Flat surfaces are called Faces.

Vertex A point where 3 or more edges intersect.
Edges Where two faces intersect.
Bases Congruent faces that are contained in //
planes.
Lateral Faces Other faces (not bases) that are
polygons.
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Common Polyhedrons

• Prism Is a polyhedron w/ 2 ? faces that are
  polygons contained in // planes.
• Name it after the shape of the base
• Regular Prism A prism whose bases are
  regular polygons.
• Cube Is a prism in which all faces are
  squares.

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Pyramid

• Is a polyhedron that has all faces except one
  intersecting _at_ 1 point.
• Name it after the shape of its base.

Triangular Pyramid
Base
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Cylinder

• Is a 3D solid with ? bases (Circles) in a pair of
  // planes..

r
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Cone

• Has a circular base a vertex.

r
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Sphere

• Is a set of points in space that are a given
  distance from a given point.

r
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Regular Polyhedron

• Regular Polyhedron
• All faces are ?.
• All edges are ?.
• 5 types of Regular Polyhedrons (Platonic Solids)
• Tetrahedron
• 4 Faces
• Hexahedron
• 6 Faces
• Octahedron
• 8 Faces
• Dodecahedron
• 12 Faces
• Icosahedron
• 20 Faces

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Nets of Polyhedron

• Net A 2-Dimensional Pattern that you can fold
  to form a 3-Dimensional figure.

E
A
B
D
C
A
E
D
B
F
F
C
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Ex.1 Draw the net of the following polyhedron.
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Eulers Formula

• A formula that relates the number of faces,
  vertices, edges of a polyhedron.

F V E 2
of Edges
of Vertices
of Faces
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Ex.2 Eulers Formula

• Find the of edges of a polyhedron with 6 faces
  8 vertices.

F V E 2 6 8 E 2 14 E 2 12 E
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