Surface Area of Pyramids

1
Surface Area of Pyramids

• Pyramid A polyhedron with all faces except one
  intersecting a vertex. Pyramids are named for
  their bases, which can be a polygon of any
  variety.

2
Surface Area of Pyramids

• Lateral Faces The faces that intersect at the
  vertex. For a pyramid, they are all triangles.
• Lateral Edges The edges of the lateral faces
  that have the vertex as an endpoint.
• Altitude The segment from the vertex that is
  perpendicular to the base.

3
Surface Area of Pyramids

• Axis A line segment from the vertex of a
  pyramid to the center of its base.
• Right Pyramid A pyramid in which the altitude
  and the axis are the same segment. In this case,
  the base does not have to be a regular polygon.

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Surface Area of Pyramids

• Regular pyramid A pyramid in which the altitude
  and the axis are the same segment and the base is
  a regular polygon. In a regular pyramid, each of
  the lateral faces is a congruent isosceles
  triangle.
• Slant Height The height of each lateral face of
  the pyramid. It is represented by l (lower case
  L).

5
Surface Area of Pyramids

• Lateral Area of a Regular Pyramid
• If a regular pyramid has a lateral area of L
  square units, a slant height of l units, and its
  base has a perimeter of P units, then
• L (1/2)Pl

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Example 5-1c
CAMPING A pyramidal shaped tent is put up by two
campers. The square base is 7 feet on a side and
the slant height of the tent is 7.4 feet. Find
the lateral area of the tent.
Answer 103.6 ft2
7
Surface Area of Pyramids

• Surface Area of a Regular Pyramid
• If a regular pyramid has a surface area of T
  square units, a slant height of l units, and its
  base has a perimeter of P units and an area of B
  square units, then
• T (1/2)Pl B

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Example 5-2d
Find the surface area of the regular pyramid to
the nearest tenth.
Answer 89.8 m2
9
Example 5-3f
Find the surface area of the regular pyramid.
Answer about 298.2 cm2