Surface Area and Volume of Pyramids

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Surface Area and Volume of Pyramids

• Goal Students will find the surface area and
  volume of pyramids.

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• Surface Area of Pyramids
• A pyramid is a polyhedron in which the base is a
  polygon and the lateral faces are triangles with
  a common vertex, called the vertex of the
  pyramid.
• The intersection of two lateral faces is a
  lateral edge.
• The intersection of the base and a lateral face
  is a base edge.

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• The height of the pyramid is the perpendicular
  distance between the base and the vertex, called
  the altitude.

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• Regular Pyramid
• A regular pyramid has a regular polygon for a
  base, and the segment joining the vertex and the
  center of the base is perpendicular to the base.
• The lateral faces of a regular pyramid are
  congruent isosceles triangles.

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• The slant height, l, of a regular pyramid is the
  height of a lateral face of the regular pyramid.
• Ex.1 A regular square pyramid has a height of 15
  centimeters and a base edge length of 16
  centimeters. Find the area of each lateral face
  of the pyramid.

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• The lateral area of a pyramid is the sum of the
  areas of the congruent lateral faces.
• The surface area of a pyramid is when the area of
  the base is added to its lateral area.

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• Theorem 12.4 Surface Area of a Regular Pyramid
• Lateral Area L.A.
• Surface Area
• where p is the perimeter of the base, l is the
  slant height, and B is the area of the base.

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• Ex.2 Find the surface area of the regular
  pyramid.
• Ex.3 Find the surface area of the regular
  pyramid.

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• Ex.4 Find the surface area of the regular
  pyramid.
• Ex.5 Find the surface area of the regular
  pyramid.

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• Volume of Pyramids
• Theorem 12.9 Volume of a Pyramid
• Volume
• where B is the area of the base, h is the
  height of the pyramid.

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• Ex.6 Find the volume of the solid.
• Ex.7 Find the volume of a regular square pyramid
  with base edges 40 feet long and slant height 25
  feet.

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• Ex.8 Originally, the pyramid had height 144
  meters and volume 2, 226, 450 cubic meters. Find
  the side length of the square base.

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• Ex.9 Find the volume of the solid shown.

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• Ex.10 Find the surface area of the solid shown.