1. 10-5 Surface Area of Pyramids & Cones
Geometry

2. Pyramid
Polyhedron in which the base is a polygon and the lateral faces are triangles with a common vertex.

3. Regular pyramid
Has a regular polygon for a base and its height meets the base at its center.
Slant height of a reg. pyramid is the altitude of any lateral face.

4. Lateral Area of a regular pyramid
Where l =slant height

5. S.A. of a Regular Pyramid S.A. = B= Area of the base
P= Perimeter of the base
l = slant height
S.A. = B + L.A.

6. Ex. 1
Find the lateral area & surface area of the regular pyramid shown.
ℓ= 16 in.
10 in

7. Cones
Has a circular base and a vertex that is not in the same plane as the base.
Right Cone – the ht meets the base at its center and slant ht is the distance between the vertex and a point on the base edge.

8. Lateral Area of a Right Cone

9. S.A. of a Right Cone
S.A. =
r = radius of base
l = slant height

10. Ex. 2
Find the lateral area & surface area of the right cone shown. Give your answers in terms of l
h = 15 in.
r= 8 in
Ex. Ex. 3

11. Ex. 3 Find the surface area of each composite figure
r=6 in, h= 8 in, l=12 in
8 in.

12. Assignment

13. Ex. 2
A regular pentagonal pyramid has a base with sides of length 18 inches, an apothem of about 12.4 inches and a slant height of 24 inches. Find the surface area of the pyramid.

14. Ex. 3 Finding the slant ht
#21 pg. 739