1. GEOMETRY 10.5 Surface Area of Pyramids and Cones

2. Definitions Vertex of a pyramid: the point opposite the base of the pyramid. Regular pyramid: regular polygonal base and lateral faces are congruent isosceles triangles Slant height: the distance from the vertex to a midpoint of an edge of the base

3. Diagram

4. Lateral and Surface Area of Regular Pyramids

5. Example Find the lateral area and surface area of the figure.

6. Example: Find the lateral area and surface area of a regular square pyramid with base edge length 14 cm and slant height 25 cm. Find the lateral area and surface area of a regular square pyramid with base edge length 10 m and height 10 m.

7. Example: Find the lateral area and surface area of a regular triangular pyramid with base edge length 6ft and slant height 10ft.

8. Exploring Effects of Changing Dimensions. The base edge length and slant height of the regular hexagonal pyramid are both divided by 5. Describe the effect on the surface area.

9. Example: The base edge length and slant height of the regular square pyramid are both multiplied by 2. Describe the effect on the surface area

10. More Examples:

11. Definitions: Vertex of a cone: the point opposite the base. Axis of a cone: the segment with endpoints at the vertex and the center of the base. Right cone: the axis is perpendicular to the base. Oblique cones: the axis is not perpendicular to the base. Slant height of a right cone: the distance from the vertex of a right cone to a point on the edge of the base Altitude of a cone: the perpendicular segment from the vertex of the cone to the plane of the base.

12. Diagram:

13. Lateral and Surface Area of a Right Cone:

14. Example: Find the lateral area and surface area of the following figure.

15. Example: Find the lateral area and surface area of a right cone with radius 9 cm and slant height 5 cm.

16. Example: Find the lateral area and surface area of the right cone.

17. Finding Surface Area of Composite Figures. Find the surface area of the composite figure.

18. Example: Find the surface area o the composite figure.

19. More Examples