Name:_____KEY_________________
Perimeter, Area, Volume, and Proportionality
I. Perimeter and Area
1. Consider rectangles with the dimensions in the table. Find the perimeter and area of each
rectangle. Complete the table.
Width
Length
Perimeter
Area
A
2
3
10
6
B
2
6
16
12
C
2
9
22
18
Z
3
4
14
12
Y
3
8
22
24
X
3
12
30
36
Use the table to answer questions 2-3.
2. What are the changes in the dimensions (width and length) of rectangle A and rectangle
B? Z and Y? How did the change affect the perimeter? Area?
The length is doubled. Perimeter is increased by 2x the length of the original. Area is
doubled.
3. What are the changes in the dimensions of rectangle A and rectangle C? Z and X? How
did the change affect the perimeter? Area?
The length is tripled. Perimeter is increased by 4x the length of the original. Area is
tripled.
4. Consider rectangles with the dimensions in the table. Find the perimeter and area of each
rectangle. Complete the table.
Width
Length
Perimeter
Area
A
2
3
10
6
D
4
3
14
12
E
6
3
18
18
Z
3
4
14
12
W
6
4
20
24
V
9
4
26
36
Use the table to answer questions 5-6.
5. What are the changes in the dimensions of rectangle A and rectangle D? Z and W? How
did the change affect the perimeter? Area?
The width is doubled. Perimeter is increased by 2x the width of the original. Area is
doubled.
6. What are the changes in the dimensions of rectangle A and rectangle E? Z and V? How
did the change affect the perimeter? Area?
The width is tripled. Perimeter is increased by 4x the width of the original. Area is
tripled.
7. Consider rectangles with the dimensions in the table. Find the perimeter and area of each
rectangle. Complete the table.
Width
Length
Perimeter
Area
A
2
3
10
6
F
4
6
20
24
G
6
9
30
54
Z
3
4
14
12
U
6
8
28
48
T
9
12
42
108
Use the table to answer questions 8-9.
8. What are the changes in the dimensions of rectangle A and rectangle F? Z and U? How
did the change affect the perimeter? Area?
Length and width are doubled. Perimeter is doubled. Area is 4x the original.
9. What are the changes in the dimensions of rectangle A and rectangle G? Z and T? How
did the change affect the perimeter? Area?
Length and width are tripled. Perimeter is tripled. Area is 9x the original.
Summarize your findings:
Change in
Width/Length
width or length
doubled (x 2)
Change in Perimeter
Change in Area
Increased by 2x the original
dimension
Doubled
Increased by 4x the original
dimension
Tripled
width and length
doubled (x 2)
Doubled
x4
width and length
tripled (x 3)
Tripled
x9
width or length
tripled (x 3)
Make predictions based on your findings:
Change in
Width/Length
width or length
quadrupled (x 4)
width or length x n
width and length
quadrupled (x 4)
Change in Perimeter
Change in Area
Increased by 6x the original
dimension
x4
Increased by 2(n−1)x the original
dimension
xn
x4
x 16
xn
x n2
width and length x n
II. Volume
1. Consider rectangular prisms with the given dimensions. Find the volume of each and
compare the dimensions to those of prism G to complete the table.
Width
Length
Height
Volume
Width
Change
Length
Change
Height
Change
G
2
3
4
24
—
—
—
H
2
3
8
48
—
—
x2
I
2
3
12
72
—
—
x3
J
4
3
4
48
x2
—
—
K
6
3
4
72
x3
—
—
L
2
6
4
48
—
x2
—
M
2
9
4
72
—
x3
—
Use the table to answer questions 2-3.
2. What is the change in the dimensions of prism H? J? L? How did the change affect the
volume?
One dimension is doubled. Volume is doubled.
3. What is the change in the dimensions of prism I? K? M? How did the change affect the
volume?
One dimension is tripled. Volume is tripled.
4. Consider rectangular prisms with the given dimensions. Find the volume of each and
compare the dimensions to those of prism G to complete the table.
Width
Length
Height
Volume Width
Length
Height
Change Change Change
G
2
3
4
24
—
—
—
N
2
6
8
96
—
x2
x2
O
2
9
12
216
—
x3
x3
P
4
6
4
96
x2
x2
—
Q
6
9
4
216
x3
x3
—
R
4
6
8
192
x2
x2
x2
S
6
9
12
648
x3
x3
x3
Use the table to answer questions 5-7.
5. What is the change in the dimensions of prism N? P? How did the change affect the
volume?
6. What is the change in the dimensions of prism O? Q? How did the change affect the
volume?
7. What is the change in the dimensions of prism R? S? How did the change affect the
volume?
Summarize your findings:
How many
dimensions
changed?
1
1
2
2
3
3
By what factor?
Change in Volume
x2
x3
x2
x3
x2
x3
Doubled
Tripled
x4
x9
x 8 = x 23
x 27 = x 33
Make predictions based on your findings:
How many
dimensions changed?
By what factor?
Change in Volume
1
x5
x5
2
x5
x 25 = x 52
3
x5
x 125 = x 53
2
2
3
3
one x 2
one x 3
one x 3
one x 5
one x 2
two x 3
one x 2
one x 3
one x 4
x6
x 15
x 18
x 24