Transcript Erny`s Surface Area of a Rectangular Prism - TN

Surface Area of a
Rectangular Prism
Getting Ready – Calling Stick Activity
What is the name of shape D?
A?
B?
C?
Square
A
B
C
D
Rectangle
Cube
Rectangular Prism
Getting Ready – Think – Pair – Share
What similarities and differences do you see
between any of these shapes?
Square
A
B
Cube
C
D
Rectangle
Rectangular Prism
Calculating Surface Area
A rectangular prism always has
6 sides, or faces.
____
Top
Side 2
Back
Front
Bottom
Length (L)
Side 1
Height (H)
Width (W)
Extension
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.
Internet Applet
Vocabulary
Net of a cube
Net
Back to lesson
Faces
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
Prism
Rectangular Prism
Back to lesson
Back
Vocabulary
Each side of a rectangular prism is called a face.
A rectangular prism
has six faces.
Back to lesson
Back
Example
So, how do we find the surface area of this
rectangular prism?
2
Front
=
4
cm
x
3
cm
=
12
cm
Back
Side 2
2
Back
4
=
4
cm
x
3
cm
=
12
cm
2 Top 2
4
Side 1 = 2 cm x 3 cm = 6 cm2
3 Front 3Side 3 cm Side 2 = 2 cm x 3 cm = 6 cm2
Top = 4 cm x 2 cm = 8 cm2
2 cm
4 cm
Bottom = 4 cm x 2 cm = 8 cm2
+
Bottom
Scaffolding
52 cm2
Internet Applet
Answer
Find the surface area
Calculate the area of
your rectangular prism
Summary Question – Think – Pair – Share
Find the mistake(s) in the problem below.
6
2
4 Top
Front
=
6
in
x
12
in
=
72
in
4
6
Back = 6 in x 12 in = 72 in2
Side
22
=
4
cm
x
12
cm
=
48
in
12 in Side = 4 in x 6 in = 24 in
22
=
4
cm
x
12
cm
=
48
in
Side = 4 in x 6 in
24 in
12 Front 12
2
=
24
in
Top = 6 in x 4 in
4 in Bottom = 6 in x 4 in = 24 in2
+
22
6 in
240
in
The side is not 4 x 6, = 288 in
it’s 4 x 12!!
Scaffolding
Warm Up
OBJECTIVE: SWBAT find the surface area of a rectangular prism
1. Find the area of the front, side, and top of this rectangular prism.
4
Front = 3 in x 12 in = 36 in2
12
12 Top 4
3
Front
3 inSide
12 in
Side = 3 in x 4 in = 12 in2
3
Top
4 in
= 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
Scaffolding
Summarize – Whole Class Discussion
OBJECTIVE: SWBAT find the surface area of a rectangular prism
1. Find the area of the front, side, and top of this rectangular prism.
Top
Front
3 inSide
12 in 4 in
Front
Side
Top+
= 36 in2
= 12 in2
= 48 in2
96 in2
Surface Area = 96 in2 …right?
Summarize – Whole Class Discussion
OBJECTIVE: SWBAT find the surface area of a rectangular prism
No!
1. Find the area of the front, side, and top of this rectangular prism.
Remember,
there
are
six
No!
No!
2
Front
=
36
in
sides
to
a
rectangular
No!
2No!
Side
=
12
in
prism…
No!
Top
No!
+ =and
48 Back
in2
• Front
Top
Front Side
• Side 1 and
Side
2
No!
2 No!
3
in
96
in
No!
No!
• Top
and Bottom
12 in
No!
4 in
Surface Area = 96 in2 …right?
Summarize – Whole Class Discussion
OBJECTIVE: SWBAT find the surface area of a rectangular prism
1. Find the area of the front, side, and top of this rectangular prism.
Top
Front
3 inSide
12 in 4 in
Front = 36 in2 Back = 36 in2
Side = 12 in2
Side = 12 in2
Top = 48 in2 Bottom = 48 in2
96 in2 +
96 in2
Surface Area = 192 in2
Agenda:
OBJECTIVE: SWBAT find the surface area of a rectangular prism
1)
2)
3)
4)
5)
6)
7)
Warm Up – Individual Work
Launch – Whole class discussion
Explore: Making the Equation for Surface Area –
Partner Activity
Class work
Review Class work
Summary
Exit Ticket – Individual Work to be
handed in to teacher
Launch – Whole Class Discussion
A formula uses only letters, numbers, and symbols
to find a mathematical value.
You already know area formulas for some shapes:
Width (W)
Rectangle
Are youLength
ready
for
(L)
some algebra?!
Triangle
Height (h)
Area =
LxW
Area =
½bxh
Area =
3.14 x r x r = πr2
base (b)
Circle
radius (r)
Explore
With your partner, try to write a formula to find the surface area
using l for length, w for width, and h for height.
Length (l)
Width (w)
Top
Width (w)
Length
(l)
Back
Side
2
Side 1 Height (h)
Height (h) Front
Height (h)
Bottom
Width (w)
Length (l)
Don’t forget that there
are six sides on a
rectangular prism!
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.
Scaffolding
Formula for Surface Area – Whole Class
SA =2 LH + 2 WH + 2 LW
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
Width
Scaffolding
Length
Top
Width
Back Length
Height (h)
Side
2
Side
1
Height Front
Height
Bottom
Width (w)
Length (l)
One cool thing about this equation is that
it doesn’t matter in what order you find
the area of the faces.
SA = 2 LH
WH+ +2
LW ++ 22LW
LH
2 WH
This is an example of the Commutative
Property of Addition ( a + b = b + a )
Practice
Find
area of this rectangular prism:
Let’sthe
trysurface
an example…
3
SA = 2LH + 2WH + 2LW
6
Top
4Front
6
6 cm
3
4
4 cm
Side
3 cm
2
=
48
cm
2 x 6 cm x 4 cm
+
2
=
24
cm
2 x 3 cm x 4 cm
+
2
=
36
cm
2 x 3 cm x 6 cm
108 cm2
Scaffolding
Class Work
Take a shot at solving some of
the problems on the class
work.
I’ll time you!
Class work #1
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
Back to Solutions
Class work #2
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
Back to Solutions
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
5
rectangular prism.
2
2
5
4 cm
3. If you aren’t sure about #1 or #2,
4
4
what is confusing to you about
2 cm
surface area?
5 cm
Scaffolding
Prism Surface Area Formula
Top
: lw
Bottom
: lw
Front
: hl
Back
: hl
Left
: hw
Right
: hw
: lw + lw + hl +
Total
hl + hw + hw
: 2lw + 2hl +
2hw
: 2(lw + hl + hw)
Surface Area of a Prism
21st Century Lessons
Surface Area of a Rectangular Prism
Lesson
Thanks to
Sarita Thomas
Shane Ulrich