Section 8 2 pyramids area volume
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Section 8.2 Pyramids, Area, & Volume. Pyramid. The solid figure formed by connecting a polygon with a point not in the plane of the polygon is called a pyramid. The polygonal region is called the base & the point is the vertex.

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Section 8.2 Pyramids, Area, & Volume

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Section 8 2 pyramids area volume

Section 8.2Pyramids, Area, & Volume

Section 8.2 Nack/Jones


Pyramid

Pyramid

  • The solid figure formed by connecting a polygon with a point not in the plane of the polygon is called a pyramid.

  • The polygonal region is called the base & the point is the vertex.

  • A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all congruent.

  • The slant height of a regular pyramid is the altitude from the vertex of the pyramid to the base of any of the congruent lateral faces of the regular pyramid.

  • The line segment from the vertex perpendicular to the plane of the base is the altitude.

Section 8.2 Nack/Jones


Pyramid1

Pyramid

  • In the regular pyramid, the distance l is called the slant height of the lateral surfaces of a regular pyramid.

  • Theorem 8.2.1: In a regular pyramid, the length a of the apothem of the base, the altitude h, and the slant height l satisfy the Pythagorean Theorem, that is l² = a² + h² in every regular pyramid.

l

h

a

Section 8.2 Nack/Jones


Lateralsurface area of a pyramid

LateralSurface Area of a Pyramid

  • Theorem 8.2.2: The Lateral Area L of a regular pyramid with slant height l and perimeter P of the base is given by:

    L = ½ pl

    It is simpler to find the area of one lateral face and multiply by the number of faces.

    Example 2 p. 401

Section 8.2 Nack/Jones


Total surface area

Total Surface Area

  • Theorem 8.2.3: The total area (surface area) T of a pyramid with lateral area L and base area B is given by ( the sum of the area of all its faces):

    T = L + B or T = ½ Pl + B

    Example:

    To find the total area,

    Find the slant height. Apply Pythagorean Theorem to one face:

    l ² + 2² = 6² or l = 42

    Find Lateral Area:

    L = ½Pl= ½42 (16) = 32 2

    Find the area of the Base: 6

    B = 16 l

    Total Area = 16 + 32 22

6

4

Section 8.2 Nack/Jones


Volume of a pyramid

Volume of a pyramid

  • Theorem 8.2.4: The volume V of a pyramid having a base area B and an altitude of length H is given by:

    V =1/3 Bh

    Example:

    Find the area of the base:

    B = ½aP.

    Since it is a 30-60-90 triangle,

    we know that a = 23

    B = ½ 23 (64) = 24 3

    V =1/3 Bh = 96 3 units3

=12

30

60

4

Section 8.2 Nack/Jones


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