1. The perimeter p of the square base is 4 X 7.5 ft, or 30 ft.
Surface Areas of Pyramids and Cones
LESSON 11-3
Additional Examples
Find the surface area of a square pyramid with base edges 7.5 ft and slant height 12 ft.
The perimeter p of the square base is 4 X 7.5 ft, or 30 ft.
You are given = 12 ft and you found that p = 30, so you can find the lateral area.
L.A. = p Use the formula for lateral area of a pyramid. 1 2
= (30)(12) Substitute. 1 2
= 180 Simplify.

2. Find the area of the square base.
Surface Areas of Pyramids and Cones
LESSON 11-3
Additional Examples
(continued)
Find the area of the square base.
Because the base is a square with side length 7.5 ft,
B  s2  7.52 
S.A. = L.A.  B Use the formula for surface area of a pyramid.
= 180  Substitute.
= Simplify.
The surface area of the square pyramid is ft 2.
Quick Check

3. Use the formula L.A. = p to find the lateral area of the pyramid.
Surface Areas of Pyramids and Cones
LESSON 11-3
Additional Examples
Find the lateral area of the hexagonal pyramid below. Round your answer to the nearest whole number.
Use the formula L.A. = p to find the lateral area of the pyramid. 1 2
The altitude of the pyramid, apothem of the base, and altitude of a lateral face form a right triangle, so you can use the Pythagorean Theorem to find the slant height .
= ( )2 = =

4. L.A. = p Use the formula for lateral area.
Surface Areas of Pyramids and Cones
LESSON 11-3
Additional Examples
(continued)
L.A. = p Use the formula for lateral area. 1 2
= (48)( ) Substitute. 1 2
Use a calculator.
The lateral area of the hexagonal pyramid is about 508 m2.
Quick Check

5. Find the surface area of the cone in terms of .
Surface Areas of Pyramids and Cones
LESSON 11-3
Additional Examples
Find the surface area of the cone in terms of .
S.A. = L.A. + B Use the formula for surface area of a cone.
= r r 2 Substitute the formulas for L.A. and B.
= (5)(13) (5)2 Substitute.
= Simplify.
= 90
The surface area of the cone is in.2.
Quick Check

6. Use the formula L.A. = r to find the lateral area of the cone.
Surface Areas of Pyramids and Cones
LESSON 11-3
Additional Examples
Leandre uses paper cones to cover her plants in the early spring. The diameter of each cone is 1 ft, and its height is 1.5 ft. How much paper is in the cone? Round your answer to the nearest tenth.
Use the formula L.A. = r to find the lateral area of the cone.
The cone’s diameter is 1 ft, so its radius r is 0.5 ft.
=  =  =
The altitude of the cone, radius of the base, and slant height form a right triangle. Use the Pythagorean Theorem to find the slant height .

7. L.A. = r Use the formula for lateral area of a cone.
Surface Areas of Pyramids and Cones
LESSON 11-3
Additional Examples
(continued)
Find the lateral area.
L.A. = r Use the formula for lateral area of a cone.
= (0.5) Substitute 0.5 for r and for .
Use a calculator.
The lateral area of the cone is about 2.5 ft.2
Quick Check