# Surface Area of Three-Dimensional Figures

Videos and solutions to help grade 6 students learn how to use nets to determine the surface area of three-dimensional figures.

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Common Core For Grade 6

### New York State Common Core Math Module 5, Grade 6, Lesson 18

Lesson 18 Student Outcomes

• Students determine that a right rectangular prism has six faces: top and bottom, front and back, and two sides. They determine that surface area is obtained by adding the areas of all the faces and develop the formula SA = 2lw + 2lh + 2wh.
• Students develop and apply the formula for the surface area of a cube as SA = 6s2.

Lesson 18 Classwork

Opening Exercise

a. What three-dimensional figure will the net create?
b. Measure (in inches) and label each side of the figure.
c. Calculate the area of each face, and record this value inside the corresponding rectangle.
d. How did we compute the surface area of solid figures in previous lessons?
e. Write an expression to show how we can calculate the surface area of the figure above.
f. What does each part of the expression represent?
g. What is the surface area of the figure?

Example 1
Fold the net used in the Opening Exercise to make a rectangular prism. Have the two faces with the largest area be the bases of the prism. Fill in the second row of the table below. Examine the rectangular prism below. Complete the table.

Example 2
Calculate the surface area of the given rectangular prism.

Exercises
1. Calculate the surface area of each of the rectangular prisms below.
2. Calculate the surface area of the cube.
3. All the edges of a cube have the same length. Tony claims that the formula SA = 6s2, where s is the length of each side of the cube, can be used to calculate the surface area of a cube.
a. Use the dimensions from the cube in Problem 2 to determine if Tony’s formula is correct.
b. Why does this formula work for cubes?
c. Becca doesn’t want to try to remember two formulas for surface area so she is only going to remember the formula for a cube. Is this a good idea? Why or why not?

Problem Set
1. - 4. Calculate the surface area of each figure below. Figures are not drawn to scale.

5. Write a numerical expression to show how to calculate the surface area of the rectangular prism. Explain each part of the expression.

6. When Louie was calculating the surface area for Problem 4, he identified the following:
length = 24.7 m, width = 32.3 m, and height = 7.9 m.
However, when Rocko was calculating the surface area for the same problem, he identified the following:
length = 32.3 m, width = 24.7 m, and height = 7.9 m.
Would Louie and Rocko get the same answer? Why or why not?

7. Examine the figure below.
a. What is the most specific name of the three-dimensional shape?
b. Write two different expressions for the surface area.
c. Explain how these two expressions are equivalent.

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