1. Surface Area of a Rectangular Prism
Day 2 (of 2)

2. 3 in 12 in 4 in Front = 3 in x 12 in = 36 in2 Side Front Top Side
Warm Up
OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism.
1. Find the area of the front, side, and top of this rectangular prism.
Front
= 3 in x 12 in
= 36 in2
Side
Front
Top
12 in
4 in
3 in
Side
= 3 in x 4 in
= 12 in2
Top
= 4 in x 12 in
= 48 in2
2) Find the circumference and area of a circle with radius 5 cm.
Radius = 5 cm
C = 2πr = 2 x 3.14 x 5 cm = 31.4 cm
A = πr2 = 3.14 x 5 cm x 5 cm = 78.5 cm2

3. Warm Up Front = 36 in2 Side = 12 in2 12 in 4 in 3 in Top = 48 in2 +
OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism.
1. Find the area of the front, side, and top of this rectangular prism.
Front
= 36 in2
Side
= 12 in2
Side
Front
Top
12 in
4 in
3 in
Top
= 48 in2 +
96 in2
Surface Area = 96 in2
…right?

4. Warm Up – Whole Class Review
No!
No!
OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism.
No!
No!
No!
No!
Remember, there are six faces on a rectangular prism…
Front and Back
Side 1 and Side 2
Top and Bottom
No!
1. Find the area of the front, side, and top of this rectangular prism.
No!
Front
= 36 in2
No!
Side
= 12 in2
No!
No!
Side
Front
Top
12 in
4 in
3 in
No!
Top
= 48 in2 +
96 in2
Surface Area = 96 in2
…right?

5. Surface Area is the sum of all the faces.12
Top 4 4
You can easily see all
the faces when you
make a net. 4 12 4
Side
Side
Front 3 3 3 3 12 4 4
Side
Front
Top
12 in
4 in
3 in
Bottom 4 4 12
Back 3 3 12

6. Warm Up Surface Area = 192 in2 Front = 36 in2 Back = 36 in2 Side
OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism.
For surface area, we need to find the sum the areas of all 6 faces.
1. Find the area of the front, side, and top of this rectangular prism.
Front
= 36 in2
Back
= 36 in2
Side
= 12 in2
Side
= 12 in2
Side
Front
Top
12 in
4 in
3 in
Top
= 48 in2
Bottom
= 48 in2
96 in2 +
Surface Area = 192 in2

7. Launch
A formula uses only letters, numbers, and symbols to find a mathematical value.
You already know area formulas for some shapes:
Are you ready for some algebra?!
Length (L)
Width (W)
Rectangle
Area =
L x W = LW
Area =
½ b x h = ½bh
Triangle
base (b)
Height (h)
Circle
radius (r)
Area =
3.14 x r x r = πr2

8. Explore: Equation for Surface Area
Try to write a formula to find the surface area using L for length, W for width, and H for height.
Top
Top
Side 1
Front
Height (h)
Front
Side
Side
Width (w)
Length (l)
Bottom
Don’t forget that there are six faces on a rectangular prism!
Back

9. Explore: Equation for Surface Area
SA = 2 LH
+ WH 2
+ LW 2
Area of the Front =
Length x Height
Area of the Back =
Length x Height
Area of Side 1 =
Width x Height
Area of Side 2 =
Width x Height
Area of Top =
Length x Width
Area of Bottom =
Length x Width .
Length
Width
Height
Top
Back
Side 2
Side 1
Front
Height (h)
Bottom
Width (w)
Length (l)

10. Explore SA = SA = 2 WH +2 LW + 2 LH 2 LH + 2 WH + 2 LW
One cool thing about this equation is that it doesn’t matter in what order you find the area of the faces.
SA =
SA = 2 WH +2 LW + 2 LH 2 LH
+ 2 WH
+ 2 LW
This is an example of the Commutative Property of Addition ( a + b = b + a )

11. Find the surface area of this rectangular prism:
Practice
Find the surface area of this rectangular prism:
Let’s try an example…
SA = 2LH + 2WH + 2LW
6 cm
3 cm
4 cm
Top
Front
2 x 6 cm x 4 cm
= 48 cm2
Side +
2 x 3 cm x 4 cm
= 24 cm2 + .
2 x 3 cm x 6 cm
= 36 cm2
108 cm2

12. Journal Work Take a shot at solving some of the following problems.
For problems 1 – 2 …Find the Surface Area. Show your work using the formula we generated on the previous slides:
SA = 2LH + 2WH + 2LW

13. Journal #1

14. Journal #2

15. Journal #3
Explain in words how to find the surface area of a rectangular prism.

16. Journal #4 Find the mistake(s) = 120 in2
= (6 in x 5 in) + (6 in x 5 in) + (3 in x 5 in) + (3 in x 5 in) + (6 in x 3 in) + (6 in x 6 in)
= 30 in in in in in in2
= 120 in2

17. Journal #5 – Find the surface area.

18. Journal # 6
Choose one of the following and answer on your paper:
1. Explain how to find surface area.
2. Find the surface area of this rectangular prism.
3. If you aren’t sure about #1 or #2, what is confusing to you about surface area? 5 4 2
5 cm
2 cm
4 cm