2. Surface Area: Prisms and Cylinders
(10-5)
What is surface area?
How do you find surface?
surface area – the sum of the areas of all of the bases and faces that make
a space figure (in other words, the number of square units that would cover the \
entire figure)
To find the surface area, make a net of the figure, find the area of each part of
The net, and add up all the areas of the net (in other words, find the total area
of the net)
Example: Find the surface area of the following rectangular prism using a net.
1. Draw and label a net.
2. Then, find the area of
each rectangle in the
net.
= 600
3. Add the areas.
The surface area is 600 square in. (in. 2)

3. Find the surface area of the rectangular prism using a net.
Surface Area: Prisms and Cylinders
LESSON 10-5
Additional Examples
Find the surface area of the rectangular prism using a net.
Find the area of each rectangle in the net.
Draw and label a net.
= Add the areas.
The surface area is 600 cm2.

4. Surface Area: Prisms and Cylinders
(10-5)
What is lateral area?
How do you find lateral area?
lateral area (L.A.) – the sum of the area of the lateral (side) faces
To find the lateral area: 1. add up the areas of the side faces, or 2. Use the
following formulas.
Lateral Area (L.A.) Formula (prism)
= perimeter of base (p) x height (h)
Lateral Area (L.A.) Formula (cylinder)
= Circumference of base (C) x height (h), where C = 2r
L.A.(cylinder) = p(base)h
L.A.(cylinder) = C(base)h = (2r)h

5. Surface Area: Prisms and Cylinders
(10-5)
How do you find surface area of a prism or cylinder using a formula?
Surface Area (S.A.) = Lateral Area (L.A.) + 2 Base Areas (2B)
S.A.(prism) = L.A. + 2B
S.A.(cylinder) = L.A. + 2B
Example: Find the surface area of the following triangular prism.
Step 1: Find the lateral area.
L.A. = perimeter (p) of base  height (h)
= ( )  = =
Step 2: Find the surface area.
S.A. = lateral area (L.A.) + 2 base areas (2B)
= (½ · 6 · 4) = =
The surface area of the triangular prism is 216 square cm. (cm. 2)

6. Find the surface area of the rectangular prism.
Surface Area: Prisms and Cylinders
LESSON 10-5
Additional Examples
Find the surface area of the rectangular prism.
Step 1: Find the lateral area.
L.A. = ph Use the formula for lateral area.
= ( ) p = and h = 20
= 440
Step 2: Find the surface area.
S.A. = L.A. + 2B Use the formula for surface area
= (5 • 6) L.A. = 440 and B = 5 • 6 =
= 500
The surface area of the rectangular prism is 500 in.2.

7. Surface Area: Prisms and Cylinders
(10-5)
Example: Find the surface area of the following sardine can to the nearest square centimeter.
Step 1: Find the lateral area.
L.A. = Circumference (C = 2r) of base x height (h)
= 2r · h
= 2 · 3.5 · 11.5
= 80.5
Step 2: Find the surface area.
S.A. = lateral area (L.A.) + 2 base areas (2B)
S.A. = L.A. + 2r2
= 80.5 + 2(3.5)2
= 80.5 
= 105
 330
The surface area of the can is 105 square cm. (cm.2 ) or about 330 square cm. (cm. 2).

8. Find the surface area of the cylindrical water tank.
Surface Area: Prisms and Cylinders
LESSON 10-5
Additional Examples
Find the surface area of the cylindrical water tank.
Step 1: Find the lateral area.
2 (8)(15)
 r = 8 and h = 15
L.A. = rh Use the formula for lateral area.
Step 2: Find the surface area.
S.A. = L.A B Use the formula for surface area.
= 240 (8)2
= 240  L.A. = 240p and B = p(8)2
=  368 (3.14) Use 3.14 for p. Round.
 1,156
The surface area of the water tank is about 1,156 ft2.

9. 3. cylindrical candle with radius 2 cm and height 16 cm 408 cm2
Surface Area: Prisms and Cylinders
LESSON 10-5
Lesson Quiz
Find the surface area of each figure rounded to the nearest whole unit.
1. triangular prism with base perimeter 24 cm, base area 24 cm2, and height 15 cm
2. rectangular prism with base perimeter 30 cm, base area 50 cm2, and height 150 cm
3. cylindrical candle with radius 2 cm and height 16 cm
408 cm2
4,600 cm2
about 226 cm2