1. Surface
Area
Calculate the surface area and volume of prisms and use appropriate units, such as cm2 and cm3. Justify the formulas used. Justification my involve decomposition, nets, or other models.

2. Helpful Hints Surface Area of a Prism 10.6 Notes
Surface area is found by finding the area of all the sides and then adding those answers up.
Ask yourself how many faces there are
Divide the prism into individual shapes if you need to
Draw a net of the shape if you need to
Helpful Hints

3. I can… Determine the surface area of rectangular prisms
Determine the surface area of triangular prisms
Self Assessment
5- I can do it without help & teach others.
4- I can do this with no help, but I don’t know if I can explain it.
3- I can do this with a little help.
2- I can do this with a lot of help!
1- I don’t have a clue.

4. Surface Area What does it mean to you?
Does it have anything to do with what is in the inside of the prism.?
Surface area is found by finding the area of all the sides and then adding those answers up.
How will the answer be labeled?
Units2 because it is area!

5. What are the dimensions of this rectangle?
4 cm 7 cm 10
Do you see the RED face?
What are the dimensions of this rectangle?
4 cm
10 cm

6. Do you see another face that is just like the RED face?
4 cm 7 cm 10
Do you see another face that is just like the RED face?
Where is it located?

7. Yes, it’s on the back.
10cm
4 cm

8. 40cm2
Now there are 2 rectangles
that each have an area of 40 sq. cm

9. What are the dimensions of this rectangle?
4 cm 7 cm 10
Do you see the BLUE face?
What are the dimensions of this rectangle?
4 cm
7 cm

10. Do you see another face that is just like the BLUE face?
4 cm 7 cm 10
Do you see another face that is just like the BLUE face?
Where is it located?

11. Yes, it’s on the left side.
7 cm
4 cm
4 cm
7 cm

12. 28cm2
Now there are 2 rectangles
that each have an area of 28 sq. cm.

13. Do you see the GREEN face?
4cm 7 cm
10cm
Do you see the GREEN face?
What are the dimensions of this rectangle?
7 cm
10 cm

14. Do you see another face that is just like the GREEN face?
4 cm 7 cm 10
Do you see another face that is just like the GREEN face?
Where is it located?

15. Yes, it’s on the bottom.
10cm
7 cm
10cm
7 cm

16. 70cm2
Now there are 2 rectangles
that each have an area of 70 sq. cm.

17. Now we just need to add all the areas of the sides together.+
70cm2
28cm2
40cm2

18. The total Surface Area for this rectangular prism is=
276cm2

19. Opposite faces are the same.
Rectangular Prism
front
top
side
4 in
5 in
6 in
How many faces are on here? 6
Find the area of each of the faces.
Do any of the faces have the same area?
front = x 4 = 20
If so, which ones?
back = x 4 = 20
Opposite faces are the same.
left side = x 5 = 30
right side = 6 x 5 = 30
148 in2
Find the SA
top = x 6 = 24
bottom = x 6 = 24

20. Cube 6 4 x 4 = 16 X 6 96 m2 Are all the faces the same? YES
How many faces are there? 4m 6
Find the Surface area of one of the faces.
4 x 4 = 16
Take that times the number of faces.
X 6
96 m2

21. Triangular Prism 5 = 6 x 2= 12 How many faces are there?4 5
How many of each shape does it take to make this prism?
10 m 3
2 triangles and 3 rectangles
b x h 2
4 x 3 2
Find the surface area. Start by finding the area of the triangle.
= 6 x 2= 12
How many triangles were there?
5 x 10 = 50 = side 1
4 x 10 = 40 = side 2
3 x 10 = 30 = side 3 2
Find the area of the 3 rectangles.
= 120
Total SA = = 132 m2

22. Find the surface area of the triangular prism.
Simple Method
Find the surface area of the triangular prism.
5 ft
8 ft
20 ft
10 ft

23. You can always cut the prism into individual shapes
8 ft
5 ft
10 ft
20 ft
20 ft
5 ft
8 ft
10 ft
20 ft
10 ft

24. You can always cut the prism into individual shapes
8 ft
5 ft
10 ft
20 ft
40 sq ft
20 ft
100 sq ft
5 ft
8 ft
10 ft
20 ft
10 ft
200 sq ft
40 sq ft
100 sq ft

25. 40 + 40 + 100 + 100 + 200 = 480 sq ft 40 sq ft 100 sq ft 200 sq ft

26. Nets A net is all the surfaces of a rectangular solid laid out flat.
Back
8 cm
Top
Side
Front
10 cm
8 cm
5 cm
lt. Side
Top
5 cm
Right Side
8 cm
Front
8 cm
Bottom
5 cm
10 cm

27. Each surface is a rectangle.
Find the Surface Area using nets.
Top
Side
Front
10 cm
8 cm
5 cm
Back
8 cm 80 40 40
Left Side 50
Top
Right Side
5 cm
8 cm
Front
8 cm 80
Each surface is a rectangle.
A = lw 50
Bottom
5 cm
10 cm
Find the area of each surface.
Which surfaces are the same?
Find the Total Surface Area.
340 cm2

28. Your Turn
A = s2
A = 72
A = 49 in2
7 in
S.A. = 49(6)
S.A. = 294 in2

29. Your Turn Surface area word problems: F 4x3 = 12 B 4x3 = 12
Bob is wrapping a present that is 12 inches long, 4 inches wide, and 3 inches tall. What is the minimum amount of wrapping paper required?
F x3 = 12
= 192 in²
B x3 = 12
T x 4 = 48
Bt x 4 = 48 3
LS = 12 x 3 = 36
RS = 12 x 3 = 36 12 4

30. Find the surface area of the triangular prism.
Your Turn
Find the surface area of the triangular prism.
10 ft
8 ft
22 ft
15 ft

31. 8 ft
10 ft
15 ft
22 ft
22 ft
10 ft
8 ft
15 ft
22 ft
15 ft

32. 60 sq ft 220 sq ft 330 sq ft 60 sq ft 220 sq ft

33. 60 + 60 + 220 + 220 + 330 = 890 sq ft 40 sq ft 100 sq ft 200 sq ft

34. I can… Determine the surface area of rectangular prisms
Determine the surface area of triangular prisms
Self Assessment
5- I can do it without help & teach others.
4- I can do this with no help, but I don’t know if I can explain it.
3- I can do this with a little help.
2- I can do this with a lot of help!
1- I don’t have a clue.