Surface Area of Solids
The Gift Box
ACTIVITY
6.3
SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge
My Notes
J.T. is the creative director for a paper products company. The
company is introducing a new line of gift boxes, called No
Wrapping Required, for hard-to-wrap gifts. The boxes come
in a variety of shapes, sizes, colors, and themes for birthdays,
anniversaries, and holidays.
1. Match each of the following gift boxes with the net used to
create it. Give the most appropriate geometric name for each
gift box.
Gift Boxes
ACADEMIC VOCABULARY
A solid is a three-dimensional
figure having length, width,
and height.
Nets
4m
2m
6.3 in.
7 in.
6m
4 in.
4 in.
4 in.
5 in.
© 2010 College Board. All rights reserved.
4 in.
4 in.
1 in.
7 in.
5 yd
4 yd
10 yd
5 yd
2 yd
Unit 6 • Three-Dimensional Geometry
317
ACTIVITY 6.3
Surface Area of Solids
continued
The Gift Box
SUGGESTED LEARNING STRATEGIES: Interactive Word
Wall, Identify a Subtask
My Notes
MATH TERMS
The lateral face of a prism is
any face that is not the base
of the prism. The word lateral
means “related to the side.”
A lateral face of a solid is a face that is not a base. A right
prism is a prism in which the lateral faces are rectangles and are
perpendicular to the bases.
2. Examine the right hexagonal prism below.
3 km
3 km
3 km
3 km
5 km
3 km
3 km
a. Give the dimensions of each lateral face in the solid, and
then find the area of each lateral face. Show your work.
© 2010 College Board. All rights reserved.
b. The lateral area of a solid is the sum of the areas of
the lateral faces. Find the lateral area of the solid.
Show all your work.
318
SpringBoard® Mathematics with MeaningTM Level 3
Surface Area of Solids
ACTIVITY 6.3
continued
The Gift Box
SUGGESTED LEARNING STRATEGIES: Create Representations,
Think/Pair/Share, Group Presentation
My Notes
3. Use the right triangular prism below to complete parts (a)–(f).
3 ft
4 ft
Area of a Triangle:
1 bh where b represents the
A = __
2
length of the base of the triangle
and h represents the height of
the triangle.
2 ft
a. Sketch each base and label its dimensions.
b. Sketch each lateral face and label its dimensions.
c. Find the lateral area, L, of the prism. Show all calculations.
© 2010 College Board. All rights reserved.
d. Find the perimeter of the base, P.
e. Multiply the perimeter of the base, P, times the height of the
prism, h.
f. Compare your responses to parts (c) and (e). What do
you notice?
Unit 6 • Three-Dimensional Geometry
319
ACTIVITY 6.3
Surface Area of Solids
continued
The Gift Box
SUGGESTED LEARNING STRATEGIES: Create
Representations, Look for a Pattern, Group Presentation,
Quickwrite
My Notes
4. Complete the table below using what you know about
prisms.
Lateral
Area
Prism
Labeled Sketch of
Base
Perimeter
of Base
Height of
Prism
4m
2m
6m
4 in.
4 in.
4 in.
5 in.
5 yd
4 in.
4 yd
10 yd
5 yd
2 yd
5. Use variables P, h, and L to explain how to find the lateral area,
L, of a prism.
Area of a Trapezoid:
1 h (b + b ), where b and
A = __
1
2
1
2
b 2 are the lengths of the bases of
a trapezoid and h is the height of
the trapezoid.
320
SpringBoard® Mathematics with MeaningTM Level 3
© 2010 College Board. All rights reserved.
4 in.
Surface Area of Solids
ACTIVITY 6.3
continued
The Gift Box
SUGGESTED LEARNING STRATEGIES: Identify a Subtask,
Visualization, Quickwrite
My Notes
6. Find the lateral area, L, for each of the following solids.
a.
3 in.
3 in.
3 in.
9 in.
b.
5 in.
6 in.
6 in.
9 in.
2 in.
c. a rectangular prism with height 10 mm and a square base
with side length 4 mm
WRITING MATH
Surface area is represented by
SA or by T in an expression.
© 2010 College Board. All rights reserved.
7. The surface area of a prism is the sum of the areas of the lateral
faces and the areas of the bases. Describe the relationship
between the lateral area and the surface area of a prism.
Unit 6 • Three-Dimensional Geometry
321
ACTIVITY 6.3
Surface Area of Solids
continued
The Gift Box
SUGGESTED LEARNING STRATEGIES: Identify a Subtask,
Think/Pair/Share, Group Presentation
My Notes
8. Consider these gift boxes from the first page of this activity.
4m
2
1 m = 10,000 cm
2m
2
5 yd
1 yd 2 = 9 ft 2
4 yd
3 yd
6m
1 ft 2 = 144 in. 2
10 yd
5 yd
2 yd
a. Find the surface area of each box. Show all your calculations.
b. Sometimes, you may need to express a measurement in
different units from the ones given. Express the surface area
of the above-left box in square centimeters.
c. What is the surface area of the above-right box in square feet?
a.
2.8 cm
12 cm
2.8 cm
2.8 cm
2.8 cm
CONNECT TO AP
There are many applications
of surface area and volume in
calculus.
b. A right triangular prism has a height 6 cm. The base of the
triangular base is 3 cm and the height of the triangular base
is 4 cm.
c. Express the surface area you found in 9b in square meters.
322
SpringBoard® Mathematics with MeaningTM Level 3
© 2010 College Board. All rights reserved.
9. Find the surface area for each of the following solids.