1. Section 12.3 Notes

2. Pyramids

3. Pyramids
In geometry, a pyramid is a three-dimensional figure with one base that is a polygon.
The other faces of a pyramid, called the lateral faces, are triangles that connect the base to the vertex.
The pyramid is a regular pyramid if the base is a regular polygon and the lateral faces are congruent isosceles triangles.

4. The height, h, of a regular pyramid is the distance from the vertex to the center of the base.
The slant height, s, of a regular pyramid is the altitude of a lateral face.

5. Parts of a Pyramid
vertex
lateral face h s a
base

6. Three Right Triangles Found in a Pyramid

7. #1 – A lateral face
lateral edge s
base edge

8. #2 – The triangle made by the height, apothem, and slant height.

9. #3 – The triangle made by the height, radius, and lateral edge.

10. Surface Area of Pyramids
The surface area of a pyramid is the sum of the lateral area and the area of the base.

11. Net
LA =
½ps s
base edge

12. Surface Area Formula SApyramid = ½ps + B
where p is the perimeter of the base, s is the slant height and B is the area of the base.

13. Example 1
Find the surface area of the following square pyramid. Round your slant height to the nearest whole number.
471 ft.
ft.

14. s
471 ft. a
471 ft.
ft.

16. Example 2
Find the surface area of a right pyramid whose base is an equilateral triangle with side lengths of 4 cm. And the slant height of the pyramid is 10 cm.

17. s = 10 cm
4 cm.

18. Cones
A cone is a three-dimensional figure with one circular base and a vertex.
In this unit, you will learn about right cones.

19. The vertex of a right cone is directly above the center of the base.
The height, h, of a right cone is the segment that connects the vertex with the center of the base.
The radius, r, of a right cone is the radius of the base.
The slant height, s, of a right cone is the segment from the vertex to any point on the base.

20. vertex h s r

21. Surface Area of Cones
The surface area of a cone is the sum of the lateral area and the area of the base.

22. Surface Area Formula for a Cone
SA = rs + r2
where r is the radius of the base and s is the slant height.

23. Example 3
Find the surface area of the following cone.
6 ft
2 ft