1. 12.3 Surface Area of Pyramids and Cones
Hubarth
Geometry

2. Vertex
Height
Slant
height
Base

3. Ex 1 Find the Slant Height
Find the slant height of the Rainforest Pyramid.
Round your answer to the nearest whole number.
100ft
200ft
Solution
200ft

4. Theorem 12.4
Surface Area of a Pyramid

5. Ex 2 Find the Surface Area of a Pyramid
Find the surface area of the pyramid.
4ft
Solution
6ft
6ft
1. Find the area of the base.
B= (6)(6)=36
2. Find the perimeter of the base.
P= = 24

6. Ex 3 Find the Surface Area of a Pyramid
Find the surface area of the regular hexagonal pyramid.
First, find the area of the base. Find the area of one triangle inside the
Hexagon and then times by the number of sides.
(10)(5 3 ) 2 = B= 43.3(6)=259.8
S = B Pl
= (60)(14) =
≈ 679.8

7. Theorem 12.5
Surface Area of a Cone l r

8. Ex 3 Find the Surface Area of a Cone
Find the surface area of the cone to the nearest whole number. a. b.
4in
5ft
6in
12ft
Solution

9. Ex 4 Standardized Test Practice
To find the slant height l of the right cone, use the
Pythagorean Theorem.
l2 = h2+ r 2
l2 =
l = 10
Use the formula for the surface area of a right cone.
S = πr2 + πrl
= π(62) + π(6)(10)
= 96π
The correct answer is B.

10. Find the surface area of the pyramid.
Practice
Find the surface area of the pyramid. 1. 2.
12ft
10ft 12
10ft
3. Find the surface area of the cone to the nearest whole number
3cm
4cm