1. Geometry Surface Area of Pyramids and Cones

2. December 8, 2015 Goals Know what a pyramid is. Find the surface area of a pyramid. Know what a cone is. Find the surface area of a cone.

3. December 8, 2015 Pyramids

4. December 8, 2015 Pyramid Polyhedron with a polygon base. Lateral faces are triangles. Lateral faces meet at a common vertex. Regular pyramid: base is a regular polygon. (This is what we will discuss.)

5. December 8, 2015 Square Pyramid Vertex Altitude (h) Slant Height ( l )

6. December 8, 2015 Surface Area of a Pyramid The surface area is the sum of the area of the base and the area of the lateral faces. SA = B + LA

7. December 8, 2015 Surface Area of a Pyramid Unfold the pyramid: The surface area is the sum of the area of the base and the area of the lateral faces. S

8. December 8, 2015 Lateral Area Re-arrange the triangles.

9. December 8, 2015 Lateral Area Find the area of a triangle. S ? SSSS ? l l

10. December 8, 2015 Lateral Area Find the area of four triangles. S SSS l What is 4s? Perimeter!

11. December 8, 2015 Lateral Area of a Pyramid l

12. December 8, 2015 Surface Area of a Pyramid S l Just add the area of the base to the LA.

13. December 8, 2015 Example Find the LA & the SA of the square pyramid. 12 16 B = 12 2 = 144 P = 4(12) = 48 l = 16 LA

14. December 8, 2015 Example 2 Find the surface area of the square pyramid. 8 6 B = 8 2 = 64 P = 4(8) = 32 l = ?

15. December 8, 2015 Example 2 Finding the slant height. 8 6 ? 4 l

16. December 8, 2015 Example 2 Finding the SA 8 6 7.21

17. December 8, 2015 Your Turn Find the SA of the square pyramid. 10 12

18. December 8, 2015 Finding the slant height. 10 12 5

19. December 8, 2015 Finding the surface area. 10 12 5 13

20. December 8, 2015 Example Find the lateral area. 20 18 10 14.96

21. December 8, 2015 Cones Circular base No Lateral Faces SA = B + LA Can be right or oblique

22. December 8, 2015 Cone Surface Area Cut the cone from the vertex to the base. Then around the base. You get: Circular Base Circle Sector

23. December 8, 2015 Cone Surface Area A =  r 2 Circular Base Circle Sector r l l The length of this arc is the circumference of the base. 2r2r

24. December 8, 2015 Sector Area Circle Sector l 2r2r This is the lateral area of a cone.

25. December 8, 2015 Cone Surface Area A =  r 2 Circular Base Circle Sector r l l 2r2r A =  r l SA =  r 2 +  rl

26. December 8, 2015 Cone Surface Area r l SA =  r 2 +  rl SA =  r(r + l) LA =  rl

27. December 8, 2015 Example Find the SA of the cone. 4 6 SA =  r(r + l) SA =  (4)(4 + 6) SA = 40  SA  125.66

28. December 8, 2015 Your Turn Find the SA of the cone. 5 15 SA =  (5)(5 + 15) SA =  (5)(20) SA = 100  SA  314.16

29. December 8, 2015 Example Find the SA of the cone. 8 3 l Finding l: 8.54

30. December 8, 2015 Example Find the SA of the cone. 8 3 Finding SA: SA =  r(r + l) SA =  (3)(3 + 8.54) SA =  (3)(11.54) SA  108.76 8.54

31. December 8, 2015 Your Turn Find the surface area 12 30 L 2 = 30 2 + 12 2 L  32.31 SA = π(12)(12 + 32.31) SA = 1670.45 32.31

32. December 8, 2015 Now you can find the surface area and lateral area of cone or a pyramid!

33. December 8, 2015 Summary r l S l These should be on your formula sheet.

34. December 8, 2015 Practice Problems