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Surface Area of a Rectangular Prism
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Getting Ready – Calling Stick Activity
What is the name of shape A?
A
What is the name of shape B?
C
Square Cube
Rectangle Rectangular Prism
What is the name of shape C?What is the name of shape D?
B
D
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Getting Ready – Think – Pair – Share
What similarities and differences do you see between any of these shapes?
A
C
Square Cube
Rectangle Rectangular Prism
B
D
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Side 2
Bottom
BackTop
Side 1Front
Length (L)Width (W)
Height (H)
A rectangular prism always has____ sides, or faces.6
Extension
Calculating Surface Area
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Calculating Surface Area
To help us see all six faces of a rectangular prism, mathematicians sometimes unfold the
box to see a drawing called a net.
Net of a cube Net FacesInternet Applet Vocabulary
Back to lesson
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Vocabulary
When a box is unfolded so you can see all the sides as a flat pattern, this is called it’s net.
Net of a Rectangular PrismRectangular Prism
BackBack to lesson
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Vocabulary
Each side of a rectangular prism is called a face.
A rectangular prismhas six faces.
BackBack to lesson
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So, how do we find the surface area of this rectangular prism?
4 cm2 cm
3 cm
Answer
Internet Applet
FrontSide
Top
Front = 4 cm x 3 cm = 12 cm2
= 4 cm x 3 cm = 12 cm2
= 2 cm x 3 cm = 6 cm2
= 2 cm x 3 cm = 6 cm2
= 4 cm x 2 cm = 8 cm2
= 4 cm x 2 cm = 8 cm2
52 cm2+
Scaffolding
3 34
422
BackSide 2
Bottom
Example
BackSide 1Side 2
TopBottom
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Find the surface area
Calculate the area of your rectangular prism
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Find the mistake(s) in the problem below.
Front
Top
Side
6 in
12 in
4 in
Scaffolding
6
12
46
4
12
Front = 6 in x 12 in = 72 in2
Back = 6 in x 12 in = 72 in2
Side = 4 in x 6 in = 24 in2
Side = 4 in x 6 in = 24 in2
Top = 6 in x 4 in = 24 in2
Bottom = 6 in x 4 in = 24 in2
240 in2+
The side is not 4 x 6, it’s 4 x 12!!
= 4 cm x 12 cm = 48 in2
= 4 cm x 12 cm = 48 in2
= 288 in2
Summary Question – Think – Pair – Share
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OBJECTIVE: SWBAT find the surface area of a rectangular prism
Scaffolding
Warm Up
1. Find the area of the front, side, and top of this rectangular prism.
SideFront
Top
12 in 4 in3 in
3 3 4
4 12
12 Front
Side
Top
= 3 in x 12 in
= 3 in x 4 in
= 4 in x 12 in
= 36 in2
= 12 in2
= 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
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Summarize – Whole Class DiscussionOBJECTIVE: SWBAT find the surface area of a rectangular prism
1. Find the area of the front, side, and top of this rectangular prism.
SideFront
Top
12 in 4 in3 in
FrontSideTop
= 36 in2
= 12 in2
= 48 in2
96 in2
…right?Surface Area = 96 in2
+
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1. Find the area of the front, side, and top of this rectangular prism.
Summarize – Whole Class DiscussionOBJECTIVE: SWBAT find the surface area of a rectangular prism
SideFront
Top
12 in 4 in3 in
FrontSideTop
= 36 in2
= 12 in2
= 48 in2
96 in2
+
…right?Surface Area = 96 in2
No! No!
No! No!No!No!
No!No!No! No!
No!No!
Remember, there are six sides to a rectangular prism…• Front and Back• Side 1 and Side 2• Top and Bottom
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Summarize – Whole Class DiscussionOBJECTIVE: SWBAT find the surface area of a rectangular prism
SideFront
Top
12 in 4 in3 in
FrontSideTop
= 36 in2
= 12 in2
= 48 in2
Back = 36 in2
Side = 12 in2
Bottom = 48 in2
96 in2 96 in2+
Surface Area = 192 in2
1. Find the area of the front, side, and top of this rectangular prism.
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Agenda:
1) Warm Up – Individual Work 2) Launch – Whole class discussion3) Explore: Making the Equation for Surface Area –
Partner Activity4) Class work5) Review Class work6) Summary7) Exit Ticket – Individual Work to be
handed in to teacher
OBJECTIVE: SWBAT find the surface area of a rectangular prism
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Launch – Whole Class Discussion
Are you ready for some algebra?!
A formula uses only letters, numbers, and symbols to find a mathematical value.You already know area formulas for some shapes:
Length (L)
Width (W)Rectangle
Triangle
base (b)
Height (h)
Circle radius (r)
Area = L x W
Area = ½ b x h
Area = 3.14 x r x r = πr2
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Scaffolding
Need a hint? Write the formulas for the front, side 1, and the top.Then write the formulas for the back, side 2, and the bottom.
ExploreWith your partner, try to write a formula to find the surface area using l for length, w for width, and h for height.
BackSide 2
Bottom
Side 1Front
Length (l)Width (w)
Top
Height (h) Length (l)
Length (l)
Height (h) Height (h)
Width (w) Width (w)
Don’t forget that thereare six sides on arectangular prism!
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BackSide 2
Bottom
Side 1Front
Length (l)Width (w)
Height (h)
Area of the Front =
SA = Length x Height
LH
Area of the Back = Length x HeightArea of Side 1 =Area of Side 2 =
Top
Width x Height
Length x WidthWidth x Height
Area of Top =
Length x WidthArea of Bottom =
2 + WH2 + LW2
Length
LengthWidth Width
Height Height
Scaffolding
Formula for Surface Area – Whole Class
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SA = LH WH+ 2 LW2 + 2
One cool thing about this equation is that it doesn’t matter in what order you find the area of the faces.
SA = 2 WH +2 LW + 2 LH
This is an example of the Commutative Property of Addition ( a + b = b + a )
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Find the surface area of this rectangular prism:
6 cm3 cm
4 cm
Let’s try an example…
SA = 2LH + 2WH + 2LW
Front 2 x 6 cm x 4 cm = 48 cm2
2 x 3 cm x 4 cm
Side
= 24 cm2
2 x 3 cm x 6 cm
Top
= 36 cm2
108 cm2
+
+
4 46
633
Scaffolding
Practice
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Take a shot at solving some of the problems on the class
work.
I’ll time you!
Class Work
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Class work #1
Back to Solutions
SA = 2(L x H) + 2(W x H) + 2(L x W)
SA = 2( 8 x 5 ) + 2( 4 x 5 ) + 2( 8 x 4 )
SA = 2 (40 cm2) + 2( 20 cm2) + 2( 32 cm2)
SA = 80 cm2 + 40 cm2 + 64 cm2
SA = 184 cm2
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Class work #2
Back to Solutions
SA = 2(L x H) + 2(W x H) + 2(L x W)
SA = 2( 12 x 4 ) + 2( 3 x 4 ) + 2( 12 x 3 )
SA = 2 (48 in2) + 2( 12 in2) + 2( 36 in2)
SA = 96 in2 + 24 in2 + 72 in2
SA = 192 in2
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5 cm2 cm
4 cm55
4 4
2 2
Scaffolding
Exit Ticket
On a separate piece of notebook paper to be handed in to your teacher:
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 aboutsurface area?
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Surface Area of a Prism
Prism Surface Area FormulaTop : lw
Bottom : lwFront : hlBack : hlLeft : hw
Right : hw
Total : lw + lw + hl + hl + hw + hw
: 2lw + 2hl + 2hw
: 2(lw + hl + hw)
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21st Century Lessons
Thanks to Sarita ThomasShane Ulrich
Surface Area of a Rectangular PrismLesson