This document discusses the surface areas of pyramids and cones. It defines a pyramid as having a polygon base and triangular lateral faces that meet at a vertex. The slant height is the altitude of any lateral face. To find the surface area of a pyramid, add the area of the base to the sum of the areas of the lateral faces. For a cone, the surface area equals the area of the base plus the lateral area, with the lateral area equal to pi times the radius times the slant height. Examples are given to demonstrate calculating surface areas of specific pyramids and cones using given formulas.

1. NAME ______________________________________________ DATE ____________ PERIOD _____
11-5 Surface Area: Pyramids and
Cones (Pages 578–582)
A pyramid is a solid figure that has a polygon for a base and triangles for sides,
or lateral faces. Pyramids have just one base. The lateral faces intersect at a
point called the vertex. Pyramids are named for the shapes of their bases. For
example, a triangular pyramid has a triangle for a base. A square pyramid
has a square for a base. The slant height of a pyramid is the altitude of any of
the lateral faces of the pyramid. To find the surface area of a pyramid, you must
find the area of the base and the area of each lateral face. The area of the
lateral surface of a pyramid is the area of the lateral faces (not including the
base). A circular cone is another solid figure and is shaped like some ice cream
cones. Circular cones have a circle for their base.
The surface area of a cone is equal to the area of the base, plus the lateral area of the cone.
Surface Area of
The surface area of the base is equal to ␲r 2. The lateral area is equal to ␲rᐉ, where ᐉ is the
a Circular Cone
slant height of the cone. So, the surface area of the cone, SA, is equal to ␲r 2 ϩ ␲rᐉ.
Examples Find the surface area of the given geometric solids.
a. a square pyramid with a base that b. a cone with a radius of 4 cm and a
is 20 m on each side and a slant slant height of 12 cm
height of 40 m Use the formula.
Find the surface area of the base and the lateral faces. SA ϭ ␲r2 ϩ ␲rᐉ
Base: Each triangular side: SA Ϸ ␲(4)2 ϩ ␲(4)(12)
1 1 SA Ϸ 50.3 ϩ 150.8
A ϭ s2 or (20)2 A ϭ ᎏ bh or ᎏ (20)(40)
2 2 SA Ϸ 201.1 cm2
A ϭ 400 A ϭ 400
SA ϭ 400 ϩ 4(400) Area of the base plus area
SA ϭ 2000 m2 of the four lateral sides.
Practice
Find the surface area of each solid. Round to the nearest tenth.
1. 2. 3.
18.2 m
28.7 ft 12.3 mm
10 m 10 ft 10 ft 8 mm 8 mm
4. 11.4 in. 5. 6.
21 cm
3.1 in.
15.3 in. 2.2 in. 2.2 in. 17 cm
7. Standardized Test Practice What is the surface area of a square pyramid
where the length of each side of the base is 10 meters and the slant
height is also 10 meters?
A 300 m2 B 400 m2 C 500 m2 D 1000 m2
Answers: 1. 885.9 m2 2. 674 ft2 3. 260.8 mm2 4. 548.0 in2 5. 18.5 in2 6. 2029.5 cm2 7. A
© Glencoe/McGraw-Hill 94 Glencoe Pre-Algebra