Warm Up1.) Find the area of the hexagon.

2.) If a solid has 5 faces, 8 edges, how many vertices does it have?

3.) Sketch a pentagonal pyramid.

Surface Area of Prisms12.2

VocabularyLateral Face – face that is not the base

Surface Area – the sum of the area of the faces.

Net – two-dimensional representation of the faces

Formula’sSurface area of a Right Prism

S = 2B + Ph = aP + Ph

Where a is the apothem of the base, B is the area of the base, P is the perimeter of the base, and h is the height of the prism.

EXAMPLE 1 Use the net of a prism

Find the surface area of a rectangular prism with height 2 centimeters, length 5 centimeters, and width 6 centimeters.

STEP 1

SOLUTION

Sketch the prism. Imagine unfolding it to make a net.

EXAMPLE 1

STEP 2

Use the net of a prism

Find the areas of the rectangles that form the faces of the prism.

STEP 3 Add the areas of all the faces to find the surface area.

The surface area of the prism is

S = 2(12) + 2(10) + 2(30) = 104 cm2.

EXAMPLE 2 Find the surface area of a right prism

SOLUTION

STEP 1 Find the perimeter and area of a base of the prism.

Perimeter P = 5(7.05)

Apothem a = √ 62 –3.5252

EXAMPLE 2

Find the surface area of the right pentagonal prism.

Find the surface area of a right prism

Each base is a regular pentagon.

≈ 4.86

= 35.25

EXAMPLE 2

STEP 2 Use the formula for the surface area that uses the apothem.

S = aP + Ph Surface area of a right prism

≈ (4.86)(35.25) + (35.25)(9) Substitute known values.

≈ 488.57 Simplify.

Find the surface area of a right prism

The surface area of the right pentagonal prism isabout 488.57 square feet.

ANSWER

GUIDED PRACTICE for Examples 1 and 2

1. Draw a net of a triangular prism.

SOLUTION

2. Find the surface area of a right rectangular prism with height 7 inches, length 3 inches, and width 4 inches using (a) a net and (b) the formula for the surface area of a right prism.

for Examples 1 and 2GUIDED PRACTICE

ANSWER

(a) NET: Left and right faces: 7 4 = 28 in.2

Top and bottom faces: 3 4 = 12 in.2

Front and back faces: 3 7 = 21 in.2

S = 2(28) + 2(12) + 2(21) = 122 in.2

2. Find the surface area of a right rectangular prism with height 7 inches, length 3 inches, and width 4 inches using (a) a net and (b) the formula for the surface area of a right prism.

for Examples 1 and 2GUIDED PRACTICE

ANSWER

(b) S = 2B + Ph

= 122 in.2

= 2(3 4) + 14 7

Class work1.)The diagonal of a cube is 8 units, what is

the surface area of this cube?

1.) Total surface area?

2.) 3 in a row removed?

3.) Other 3 removed?

HomeworkPage 806-807 4,5,6,7,8,13,15,23