Section 12.2 Notes

Prisms

Prism and its Parts

A prism is a three-dimensional figure, with two congruent faces called the bases, that lie in parallel planes.

The other faces of a prism, called the lateral faces, are formed by connecting the corresponding vertices of the bases.In this book, the lateral faces of prisms are rectangles.

A prism’s vertices are connected by segments called edges.

Base

Base

Edges

Lateral faceVertex

The prism on the previous slide is called a triangular prism. Prisms are classified by the shape of their bases.

NetImagine cutting the triangular prism along some of its edges, then opening and unfolding it. The resulting plane figure is called a net.

Net of triangular prism

Surface Area of Prisms

Surface Area

The surface area is the area of the net for a three-dimensional figure. It is abbreviated SA.

Lateral AreaThe lateral area is the area of the lateral faces (sides). It is abbreviated LA.

Lateral Area of a Prism

LA = ph,

where p = the perimeter of the base and h = the height of the prism.

The height of a prism is the length of a lateral edge.

Surface Area of a Prism

SA = LA + area of bases

= ph + 2B

Example 1

Find the SA of a triangular prism with an isosceles triangle as a base and a height of 6 cm.

13 cm 13 cm

10 cm

13 cm 13 cm

10 cm

2

2

113 13 10 6 2 12 10

2

336 cm

SA ph B

h = 6 cm.

Example 2Find the surface area to the nearest tenth of pentgonal prism with a regular pentagon as a base and a height of 10 ft.

6 ft.

6 ft.a

36

3tan36

3

tan364.1291

a

a

a

2

15 6 10 2 4.1291 30

2

423.9 ft.

SA ph B

Example 3

Find SA of a hexagonal prism with a regular hexagon as a base with side length of 10 yds. and a height of 12 yds.

10 yds.

h = 12 yds.

10 yds.

h = 12 yds.

2

5 3

16 10 12 2 60 5 3

2

720 300 3 yds

a

SA

a30

Example 4Find the surface area of a prism with regular hexagonal bases with an apothem of 6.9 cm, each base edge has a length of 8 cm, and the prism has a height of 10 cm.

2

16 8 10 2 48 6.

811.2 c

9

m

2SA

Example 5Find the surface area of a right prism whose bases are equilateral triangles with side length of 4 cm. And the height of the prism is 10 cm.

4 cm

h = 10 cm

2

2 2 3

33

1 2 33 4 10 2 12

2 3

120 8 3 cm

a

SA

4 cm

h = 10 cm

a60

Cylinders

CylinderA cylinder is a figure in space whose bases are circles of the same size. The height of cylinder is the distance from the center of one base to the center of the other base.

Base

height

Net of a Cylinder

LA = Chh

Surface Area of Cylinders

Surface Area of a Cylinder

The surface area of a cylinder is the sum of the lateral area and the area of the bases.

Surface Area FormulaSA = 2πrh + 2πr2, where r is the radius of the bases and h is the height of the cylinder.

Example 6

Find the surface area of the cylinder.

2 cm.

C = 20 cm.

2

2

2

2 2

20 2 2 10

240 cm

SA rh r

r = 10 cm.

Example 7

10 cm

6 cm.

Find the surface area of this right cylinder.

2

2

2 2

2 6 10 2 36

192 cm

SA rh r

Example 8Find the surface area of a cylinder with a diameter of 10 cm. and a height of 5 cm.

2

2

2

2 2

10 5 2 5

100 cm

SA rh r