Section 12-2 Pyramids.

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Presentation transcript:

Section 12-2 Pyramids

pyramid Has only one base, which is a polygon, and for lateral faces triangles with a common vertex Vertex Base

The lateral faces intersect in segments called lateral edges.

The segment from the vertex perpendicular to the base Altitude of a pyramid The segment from the vertex perpendicular to the base The length of the altitude is the height of the pyramid!

altitude

A pyramid is named by the shape of its base.

Examples Triangular Pyramid Square Pyramid Hexagonal Pyramid Pentagonal Pyramid

Properties of Regular pyramids The base is a regular polygon. All lateral edges are congruent. All lateral faces are congruent isosceles triangles. The height of a lateral face is called the slant height (l ) of the pyramid. The altitude meets the base at its center.

Theorem 12-3 The lateral area of a regular pyramid equals half the perimeter of a base times the slant height.

Total Area T.A. = L.A. + B

Theorem 12-4 The volume of a pyramid equals one-third the area of the base times the height of the pyramid.

Slant Height Height of Pyramid

Slant Height Lateral edge