Surface Area of a Rectangular Prism

8/11/2019 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 ReadyThink 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

Back

Top

Side 1

Front

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 rectangularprism, mathematicians sometimes unfold the

box to see a drawing called a net.

Net of a cube Net Faces

Internet Applet Vocabulary

Back to lesson
http://www.geogebra.org/en/upload/files/english/Knote/Nets/cube.htmlhttp://www.geogebra.org/en/upload/files/english/Knote/Nets/cube.html


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Vocabulary

When a box is unfolded so you can see all thesides as a flat pattern, this is called its 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 prism

has 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 cm

2

52 cm2+

Scaffolding

3 34

422

BackSide 2

Bottom

Example

Back

Side 1Side 2

Top

Bottom
http://www.learnalberta.ca/content/memg/index.html?term=Division02/Surface_Area/index.html


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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

S

ide

6 in

12 in

4 in

Scaffolding

6

12

464

12

Front = 6 in x 12 in = 72 in2

Back = 6 in x 12 in = 72 in2

Side = 4 in x 6 in = 24 in2Side = 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,

its 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

33

44

1212

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 = 2r = 2 x 3.14 x 5 cm = 31.4 cm

A = r2= 3.14 x 5 cm x 5 cm = 78.5 cm2


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SummarizeWhole Class Discussion



SideFront

Top

12 in 4 in

3 in

FrontSide

Top

= 36 in2

= 12 in2

= 48 in2

96 in2

right?Surface Area = 96 in2

+


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SideFront

Top

12 in 4 in

3 in

FrontSide

Top

= 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 s ix

sides to a rectangular

prism

Front and Back

Side 1 and Side 2

Top and Bottom


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SideFront

Top

12 in 4 in

3 in

FrontSide

Top

= 36 in2

= 12 in2

= 48 in2

Back = 36 in2

Side = 12 in2

Bottom = 48 in2

96 in2 96 in2+

Surface Area = 192 in2



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Agenda:

1) Warm UpIndividual Work

2) LaunchWhole class discussion

3) Explore:Making the Equation for Surface Area

Partner Activity4) Class work

5) Review Class work

6) Summary

7) Exit TicketIndividual Work to behanded in to teacher



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Launch Whole Class Discussion

Are you ready forsome 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 = b x h

Area = 3.14 x r x r = r2


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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.

Explore

With your partner, try to write a formula to find the surface area

using lfor length, wfor width, and hfor 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)

Dont forget that there

are six sides on a

rectangular 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 Height

Area of Side 1=

Area of Side 2=

Top

Width x Height

Length x Width

Width x Height

Area of Top=

Length x WidthArea of Bottom=

2 + WH2 + LW2

Length

LengthWidth Width

Height Height

Scaffolding

Formula for Surface AreaWhole Class


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SA = LH WH+ 2 LW2 + 2

One cool thing about this equation is that

it doesnt 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

Lets 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 4

6

6

33

Scaffolding

Practice


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Take a shot at solving some ofthe problems on the class

work.

Ill time you!

Class Work
http://www.online-stopwatch.com/full-screen-stopwatch/


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Class work #1

Back toSolutions

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 toSolutions

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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5cm 2 cm

4cm55

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 thisrectangular prism.

3. If you arent sure about #1or #2,

what is confusing to you about

surface area?


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Surface Area of a Prism

Prism Surface Area Formula

Top : lw

Bottom : lw

Front : hl

Back : hl

Left : hw

Right : hw

Total: lw + lw + hl +hl + hw + hw

: 2lw + 2hl +2hw

: 2(lw + hl + hw)


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21stCentury Lessons

Thanks to

Sarita ThomasShane Ulrich

Surface Area of a Rectangular Prism

Lesson

Documents

Surface Area of a Rectangular Prism