Surface Area of a Rectangular Prism

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

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

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

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

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

Vocabulary

Each side of a rectangular prism is called a face.

A rectangular prismhas six faces.

BackBack to lesson

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

Find the surface area

Calculate the area of your rectangular prism

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

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

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

+

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

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.

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

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

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!

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

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 )

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

Take a shot at solving some of the problems on the class

work.

I’ll time you!

Class Work

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

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

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?

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)

21st Century Lessons

Thanks to Sarita ThomasShane Ulrich

Surface Area of a Rectangular PrismLesson