1. Warm Up 1.) 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.

2. Surface Area of Prisms
12.2

3. Vocabulary Lateral Face – face that is not the base
Surface Area – the sum of the area of the faces.
Net – two-dimensional representation of the faces

4. Formula’s Surface 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.

5. 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.

6. EXAMPLE 1
Use the net of a prism
Find the areas of the rectangles that form the faces of the prism.
STEP 2
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.

7. Find the surface area of a right prism
EXAMPLE 2
EXAMPLE 2
Find the surface area of a right prism
Find the surface area of the right pentagonal prism.
SOLUTION
STEP 1
Find the perimeter and area of a base of the prism.
Each base is a regular pentagon.
Perimeter P = 5(7.05)
= 35.25
Apothem a = √ 62 –3.5252
≈ 4.86

8. Find the surface area of a right prism
EXAMPLE 2
Find the surface area of a right prism
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. ≈
Simplify.
The surface area of the right pentagonal prism is
about square feet.
ANSWER

9. GUIDED PRACTICE
for Examples 1 and 2
1. Draw a net of a triangular prism.
SOLUTION

10. GUIDED PRACTICE
for Examples 1 and 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.
ANSWER
(a) NET: Left and right faces:
= 28 in.2
Top and bottom faces:
= 12 in.2
Front and back faces:
= 21 in.2
S = 2(28) + 2(12) + 2(21) = 122 in.2

11. GUIDED PRACTICE
for Examples 1 and 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.
ANSWER
(b) S = 2B + Ph =
2(3 4)
= 122 in.2

12. Class work
1.)The diagonal of a cube is 8 units, what is the surface area of this cube?

13. 1.) Total surface area?
2.) 3 in a row removed?
3.) Other 3 removed?

14. Homework
Page ,5,6,7,8,13,15,23