NAME _____________________________________________ DATE ____________________________ PERIOD _____________
12-2 Study Guide and Intervention
Surface Areas of Prisms and Cylinders
Lateral and Surface Areas of Prisms In a solid figure, faces that are not bases are
lateral faces. The lateral area is the sum of the area of the lateral faces. The surface
area is the sum of the lateral area and the area of the bases.
Lateral Area
of a Prism
If a prism has a lateral area of L square units, a height of h units,
and each base has a perimeter of P units, then L = Ph.
Surface Area
of a Prism
If a prism has a surface area of S square units, a lateral area of
L square units, and each base has an area of B square units,
then S = L + 2B or S = Ph + 2B
Example: Find the lateral and surface area of the regular pentagonal prism above if each base has a perimeter of
75 centimeters and the height is 10 centimeters.
L = Ph
Lateral area of a prism
= 75
(10) P = 75, h = 10
= 750
Multiply.
S = L + 2B
1
= 750 + 2(2 𝑎𝑃)
7.5
= 750 + (tan 36°)(75)
≈ 1524.2
7.5
𝑎
7.5
= tan 36°
tan 36° =
a
The lateral area is 750 square centimeters and the surface area is about 1524.2 square centimeters.
Exercises
Find the lateral area and surface area of each prism. Round to the nearest tenth if necessary.
1.
2.
3.
4.
5.
6.
Chapter 12
12
Glencoe Geometry
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
12-2 Study Guide and Intervention (continued)
Surface Areas of Prisms and Cylinders
Lateral and Surface Areas of Cylinders A cylinder is a solid with bases that are
congruent circles lying in parallel planes. The axis of a cylinder is the segment with
endpoints at the centers of these circles. For a right cylinder, the axis is also the altitude
of the cylinder.
Lateral Area
of a Cylinder
If a cylinder has a lateral area of L square units, a height of h units, and a base
has a radius of r units, then L = 2πrh.
Surface Area
of a Cylinder
If a cylinder has a surface area of S square units, a height of h units, and a
base has a radius of r units, then S = L + 2B or 2πrh + 2πr2.
Example: Find the lateral and surface area of the cylinder. Round to the nearest tenth.
If d = 12 cm, then r = 6 cm.
L = 2πrh
= 2π(6)(14)
≈ 527.8
S = 2πrh + 2𝜋𝑟 2
≈ 527.8 + 2𝜋(6)2
Lateral area of a cylinder
r = 6, h = 14
Use a calculator.
Surface area of a cylinder
2πrh ≈ 527.8, r = 6
≈ 754.0
Use a calculator.
The lateral area is about 527.8 square centimeters and the surface area is about 754.0 square centimeters.
Exercises
Find the lateral area and surface area of each cylinder. Round to the nearest tenth.
1.
2.
3.
4.
5.
6.
Chapter 12
13
Glencoe Geometry