1. 10-4 Surface Area of Pyramids and Cones
5/25/17
PYRAMID: a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex (called the vertex of the pyramid)
ALTITUDE: of a pyramid is the perpendicular segment from the vertex to the base (the height h of the pyramid)

2. In this class, assume a pyramid is regular unless otherwise stated.
REGULAR PYRAMID: base is a regular polygon and lateral faces are congruent isosceles triangles
SLANT HEIGHT: l is the length of the altitude of a lateral face of the pyramid
LATERAL AREA of a pyramid is the sum of the area of the congruent lateral faces.
Vertex
Lateral edge
Lateral face l
BASE

3. l l l l l (p is the perimeter of the base)
LATERAL AND SURFACE AREAS OF
REGULAR PYRAMIDS
L.A. = ½ p
S.A. = ½ p + area of base
= slant height
Ex: Find the surface area of the hexagonal pyramid.
S.A. = ½ pl + ½ (ap)
= ½ (36)(9) + ½ (3 3)(36) in
Calc = in2 in
6 in
1) Find surface area of a square pyramid with base edges 5 m and slant height 3 m. l l l l l
S.A. = ½ (20)(3) + 52 = 55 m2

4. RIGHT CONE: the altitude is a perpendicular segment from the vertex to the center of the base. The slant height l is the distance from the vertex to a point on the edge of the base.
slant height l altitude (h) h r
base
The lateral area is ½ the circumference of the base times the slant height.
LA = ½ Cl

5. l l l l l LATERAL AND SURFACE AREAS OF A CONE L.A. = r S.A. = r + r2 r
NOTE: C = 2πr, so LA = ½(2πr)l = πrl
LATERAL AND SURFACE AREAS OF A CONE
L.A. = r
S.A. = r r2 r
Ex: Find the surface area of the cone in terms of .
S.A. = r + r2
= (15)(25) + (15) cm =
= cm cm
r = 22 m
= 10 m l l l l l
S.A. = π(22)(10) + π(22)2 =
220π + 484π =
704π cm2

6. Find the slant height of a square pyramid with base edges 12 cm and altitude 8 cm.
Find the lateral area of the regular square pyramid.
7 in
4 in
Find the surface area of the pyramid whose base is a regular hexagon. Round to the nearest whole number.
4) Find the surface area of a cone with radius 8 cm and slant height 17 cm in terms of .
6 – 8 - ?? (Triple…) 6 – 8 – 10. Slant height = 10
LA = ½ pl =
½ (16)(7) = 56 in2
LA = ½ pl =
14 ft base edge
½ (84)(24) = 1008 ft2
7√3 ft apothem
SA = ½ ap =
24 ft slant height
SA = ½ (7√3)(84) = 1517 ft2
S.A. = π(8)(17) + π(8)2 = 200π cm2

7. Assignment: Page 540 #2 – 20 even, 46, 47