1. Lesson 12-2 Pyramids (page 482)
Essential Question
How can you calculate the area and volume of a pyramid?

3. Pyramids around the world

4. Pyramid in the U.S.A.

5. Pyramid Arena in Memphis, Tennessee
Pyramid in the U.S.A.
Pyramid Arena in Memphis, Tennessee

14. 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.

15. triangular pyramid

16. triangular pyramid

17. rectangular pyramid

18. rectangular pyramid

19. … 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).

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

21. 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 .

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

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

24. Net for a square pyramid
base

25. Net for a square pyramid
base

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

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

28. 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.

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

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

31. V = ⅓ Bh Class Demonstration: Prism and Pyramid with equal height and
congruent bases.

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

33. Example: Draw a square pyramid with a height 12
Example: Draw a square pyramid with a height 12 and a slant height of 13. Then find its lateral area, total area, & volume. 12 13 5
s = 10

34. 12 13 5
s = 10

35. 12 13 5
s = 10

36. How can you calculate the area and volume of a pyramid?
Assignment
Written Exercises on pages 485
REQUIRED: 1, 7, 9, 11, 15
BONUS: Calculator Key-In on page 488
How can you calculate the area and volume of a pyramid?