1. Lesson 12-2 Pyramids (page 482) Essential Question How is the surface area and volume of pyramids different from prisms?

3. Pyramids around the world

4. Pyramid in the U.S.A.

5. Pyramid Arena in Memphis, Tennessee

12. Pyramid A pyramid has only one base. Pyramids are named for their base, ie. triangular pyramid rectangular pyramid pentagonal pyramid hexagonal pyramid octagonal pyramid etc.

13. triangular pyramid

15. rectangular pyramid

17. … Pyramids The lateral faces of a pyramid are triangles. The segments in which the lateral faces intersect are the lateral edges. The vertex of a pyramid is where all the lateral edges intersect. An altitude is the segment from the vertex perpendicular to the plane of the base. The height is the length of an altitude (h).

18. pyramid altitude vertex base base edge lateral face lateral edge

19. A regular pyramid has a regular polygon as its base. Regular pyramids have the following important properties: The base is a regular polygon. All lateral edges are congruent. All lateral faces are congruent isosceles triangles. The slant height ( ℓ ) is the height of a lateral face. The altitude meets the base at its center.

20. regular pyramid altitude vertex slant height regular polygon base edge center

21. regular pyramid altitude slant height base edge radius of regular polygon apothem of regular polygon

22. Net for a square pyramid base

23. Net for a square pyramid base

24. NOTE: The lateral faces are all congruent triangles. slant height of pyramid L.A. = ½ b  h = ½ p  ℓ Perimeter of base

25. The lateral area of a regular pyramid equals half the perimeter of a base times the slant height. Theorem 12-3 L.A. = ½ p  ℓ

26. Also, if F = the area of a lateral face, then: L.A. = n F Remember the “n” is the number of sides of a polygon.

27. TOTAL AREA of a PYRAMID Remember a pyramid has only one base. T.A. = L.A. + B B = base area

28. The volume of a pyramid equals one-third the area of a base times the height of the pyramid. Theorem 12-4 V = ⅓ B  h

29. Class Demonstration: Prism and Pyramid with equal height and congruent bases.

30. Example: Draw a square pyramid with a height 12 and a slant height of 13. Then find its lateral area, total area, & volume.

31. 12 13 5 s = 10

32. 12 13 5 s = 10

33. 12 13 5 s = 10

34. Assignment Written Exercises on pages 485 GRADED: 7, 11, 15 BONUS: Calculator Key-In on page 488 How is the surface area and volume of pyramids different from prisms?