1. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Warm Up
Find the perimeter and area of
each polygon.
1. a rectangle with base 14 cm and height
9 cm
2. a right triangle with 9 cm and 12 cm
legs
3. an equilateral triangle with side length
6 cm
P = 46 cm; A = 126 cm2
P = 36 cm; A = 54 cm2

2. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Learn and apply the formula for the
surface area of a prism.
Learn and apply the formula for the
surface area of a cylinder.
Objectives

3. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Example 3: Finding Surface Areas of Composite
Three-Dimensional Figures
Find the surface area of the composite figure.

4. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Example 3 Continued
Two copies of the rectangular prism base are
removed. The area of the base is B = 2(4) = 8 cm2.
The surface area of the rectangular prism is
.
.
A right triangular prism is added to the
rectangular prism. The surface area of the
triangular prism is

5. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
The surface area of the composite figure is the sum
of the areas of all surfaces on the exterior of the
figure.
Example 3 Continued
S = (rectangular prism surface area) + (triangular
prism surface area) – 2(rectangular prism base area)
S = 52 + 36 – 2(8) = 72 cm2

6. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 3
Find the surface area of the composite figure.
Round to the nearest tenth.

7. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 3 Continued
Find the surface area of the composite figure.
Round to the nearest tenth.
The surface area of the rectangular prism is
S =Ph + 2B = 26(5) + 2(36) = 202 cm2.
The surface area of the cylinder is
S =Ph + 2B = 2(2)(3) + 2(2)2 = 20 ≈ 62.8 cm2.
The surface area of the composite figure is the sum
of the areas of all surfaces on the exterior of the
figure.

8. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
S = (rectangular surface area) +
(cylinder surface area) – 2(cylinder base area)
S = 202 + 62.8 — 2()(22) = 239.7 cm2
Check It Out! Example 3 Continued
Find the surface area of the composite figure.
Round to the nearest tenth.

9. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Always round at the last step of the problem. Use
the value of  given by the  key on your
calculator.
Remember!

10. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Example 4: Exploring Effects of Changing Dimensions
The edge length of the cube is tripled. Describe
the effect on the surface area.

11. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Example 4 Continued
original dimensions: edge length tripled:
Notice than 3456 = 9(384). If the length, width, and
height are tripled, the surface area is multiplied by 32,
or 9.
S = 6ℓ2
= 6(8)2 = 384 cm2
S = 6ℓ2
= 6(24)2 = 3456 cm2
24 cm

12. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 4
The height and diameter of the cylinder are
multiplied by . Describe the effect on the
surface area.

13. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
original dimensions: height and diameter halved:
S = 2(112) + 2(11)(14)
= 550 cm2
S = 2(5.52) + 2(5.5)(7)
= 137.5 cm2
11 cm
7 cm
Check It Out! Example 4 Continued
Notice than 550 = 4(137.5). If the dimensions are
halved, the surface area is multiplied by

14. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Example 5: Recreation Application
A sporting goods company sells tents in two
styles, shown below. The sides and floor of each
tent are made of nylon.
Which tent requires less nylon to manufacture?

15. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Example 5 Continued
Pup tent:
Tunnel tent:
The tunnel tent requires less nylon.

16. Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 5
A piece of ice shaped like a 5 cm by 5 cm by 1 cm
rectangular prism has approximately the same
volume as the pieces below. Compare the surface
areas. Which will melt faster?
The 5 cm by 5 cm by 1 cm prism has a surface area of
70 cm2, which is greater than the 2 cm by 3 cm by
4 cm prism and about the same as the half cylinder. It
will melt at about the same rate as the half cylinder.