This document provides instruction on calculating the surface area of various three-dimensional shapes using nets. It begins with an overview of surface area and reviews formulas for finding the area of rectangles and triangles. Methods for finding surface area are demonstrated for rectangular prisms, cubes, and rectangular pyramids using both decomposition into individual faces and representation via nets. Students are assigned practice problems on surface area and a final project to create practice problems and a vocabulary "tag cloud".

1. Surface
Area
cubes,
rectangular prisms,
rectangular pyramids,
& their nets

2. Common
Core
Georgia
Performance
Standards
MCC6.G.4.
Represent 3-dimensional
figures using nets made
up of rectangles and
triangles, and use the
nets to find the surface
area of these figures.
www.georgiastandards.org

3. Prior-knowledge…
Solid classification (naming the solid)
 Views:
 Top/Bottom, Front/Back, Sides
 Base, faces

4. Quick Area Review…
Rectangle
Formula: A = (b ∙ h)
Triangle

8 in
3 in
5 cm
4 cm
Substitute: A = (8 in ∙ 3 in)
Multiply: A = 24 in2
Divide by 2: A = 10 cm2

5. What is Surface AREA?
The of the
2-dimensional polygons
on the surface of a 3-d
solid. (Think of wrapping a box)
***The sum of all areas.

6. Surface Area of
Rectangular Prims
Top:
A = b ∙ h
A = 10 in ∙ 4 in
A = 40 in2
10 in
4 in
Calculate the area of
the top face:
5 in
Multiply the area of the Top face times 2 to get
the total surface area of the top and the bottom
faces. A = 80 in2

7. Top/Bottom:
A = 10 in ∙ 4 in
A = 40 in2
A = 40 ∙ 2
A = 80 in2
10 in
4 in
5 in
Rectangular Prism cont.
Front/Back:
A = 10 in ∙ 5 in
A = 50 in2
A = 50 ∙ 2
A = 100 in2
Side/Side:
A = 4 in ∙ 5 in
A = 20 in2
A = 20 ∙ 2
A = 40 in2
Sum all areas
80 + 100 + 40
SA = 220 in2

8. A = 81
A = 81
A = 63A = 63 A = 63
A = 63
Method 1:
Add the area of
each face to
calculate the
nets total
surface area.
Surface Area of a Rectangular Prism
using a net…
http://www.korthalsaltes.com/gif1/rectangular-prism-cuboid-color.gif

9. 9 cm
7 cm
9 cm
Orange: Side/Side
A = b ∙ h
A = 9cm ∙ 7cm
A = 63cm2 ∙ 2
SA = 126cm2
Yellow: Top/Bottom
A = b ∙ h
A = 9cm ∙ 7cm
A = 63cm2 ∙ 2
SA = 126cm2
Surface Area using
a net… Method 2:
Area of
each pair
of faces
Blue: Front/Back
A = b ∙ h
A = 9cm ∙ 9cm
A = 81cm2 ∙ 2
SA = 162cm2

10. 9 cm
9 cm
7 cm
Calculate the
Surface Area cont.
Sum:
SA = 126 + 126 + 162
SA = 414 cm2
http://www.korthalsaltes.com/gif1/rectangular-prism-cuboid-color.gif

11. Surface Area of a
Cube…
A cube has 6 equal faces.
4 in
SA = 6s2
SA = 6(4in) 2
SA = 6(16in2)
SA = 96in2
SA = 6(b ∙ h)
SA = 6(4in ∙ 4in)
SA = 6(16in2)
SA = 96in2
OR

12. Surface Area of a Rectangular
Pyramid using a net…
3mm
4mm
Image retrieved from http://www.math-salamanders.com/images/math-shapes-square-based-pyramid-net-2.gif

13. Step 3: Sum all areas
A = 6mm2
6mm2
6mm2
6mm2
+ 9mm2
SA = 33mm2
Surface Area of a Rectangular
Pyramid using a net…
Image retrieved from http://www.math-salamanders.com/images/math-shapes-square-based-pyramid-net-2.gif

14. Time to Practice!
Class:
IXL
AAA Math
Maisonet Math
Individual:
Study Island (10 - SA questions)

15. Final Assignment
 Part 1: With a partner, you will create a Tag
Cloud to represent the vocabulary learned
using at least 2 of the following: websites,
videos, or interactive practice. Minimum of 5
vocabulary words.
 Part 2: With your partner, create 3- 4 surface
area problems. The problems must include
the work and the final answer. Must have a
combination of problems consisting of nets,
solids, and word problems.

16. Rubric
Objective Needs Improvement
3 points
Meets Expectations
4 points
Excellent
5 points
Tag Cloud Less than 5 vocabulary words
used; most words relate to
surface area.
5 vocabulary words used; all
words relate to surface area.
More than 5 words used; all
words relate to surface area.
Tag Cloud 1 out of 3 formats used: website,
video, or interactive practice
2 out of 3 formats used: website,
video or interactive practice
3 out of 3 formats used: website,
video, and interactive practice
Written
Problems
Created less than 3 surface area
problems.
Created 3- 4 surface area
problems.
Created more than 4 surface
area problems
Written
Problems
Created problems using only 1
format: net, solid, or word
problem.
Created problems using only 2
formats: net, solid, or word
problem.
Created problems using all 3
formats: net, solid, and word
problem.
Evidence of
understanding
Final project reflects little
evidence of understanding of
surface area.
Final project reflects
understanding of surface area.
Final project reflects
understanding of surface area.
Total