1. Section 12-2
Pyramids

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

3. The lateral faces intersect in segments called lateral edges.

4. 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!

5. altitude

6. A pyramid is named by the shape of its base.

7. Examples Triangular Pyramid Square Pyramid Hexagonal Pyramid
Pentagonal Pyramid

8. 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.

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

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

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

12. Slant Height
Height of Pyramid

13. Slant Height
Lateral edge