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Math Problems
Algebra 1
Area and perimeter: word problems
62
62
62
) During a blizzard, Zeke shovels snow from the sidewalk in front of his house. The sidewalk is
26
2
3
26 \frac{2}{3}
26
3
2
yards long. Before breakfast, Zeke shovels
1
3
\frac{1}{3}
3
1
of the sidewalk. After breakfast, Zeke shovels the remaining portion
3
1
3
3 \frac{1}{3}
3
3
1
yards per hour. How many hours and minutes does it take Zeke to finish the driveway?
\newline
Sidewaik
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A square playground has sides that are
42
meters
42\,\text{meters}
42
meters
long. What is the playground's perimeter?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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A playing card is
8
centimeters
8\,\text{centimeters}
8
centimeters
tall and
6
centimeters
6\,\text{centimeters}
6
centimeters
wide. What is its area?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
square centimeters
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The perimeter of a square painting is
12
12
12
feet. How long is each side of the painting?
\newline
_____ feet
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The perimeter of a rectangular hotel room is
50
50
50
feet. It is
15
15
15
feet long. How wide is it?
\newline
\newline
_
_
_
_
\_\_\_\_
____
feet
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Each side of a square sticky note is
5
5
5
centimeters long. What is the sticky note's perimeter?
\newline
\newline
_
_
_
_
\_\_\_\_
____
centimeters
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An electrician plans to install solar panels on a rectangular section of roof with an area of
A
A
A
square meters. This width of this section of roof is
W
W
W
meters across. What is the length of this section of roof?
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Mandy's dining room is
5
meters
5\,\text{meters}
5
meters
wide and
8
meters
8\,\text{meters}
8
meters
long. Mandy wants to install a new wood floor. It will cost $\(1\).\(00\) per square meter. How much will Mandy's new floor cost?
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A rectangular garage is
12
12
12
yards long and
4
4
4
yards wide. It costs
$
3.00
\$3.00
$3.00
per square yard to put in a new concrete floor. How much would it cost to put a new concrete floor in the garage?
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Each face of a cube has an area of
4
4
4
square units. What is the volume of the cube?
\newline
____ cubic units
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A cube-shaped box has a volume of
64
cubic inches
64\,\text{cubic inches}
64
cubic inches
. What is the area of one of its faces?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
square inches
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A picture frame has an area of
121
square centimeters
121\,\text{square centimeters}
121
square centimeters
. Assuming it is a square, what is the perimeter of the frame?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
centimeters
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A cube has
6
6
6
faces, each with an area of
16
16
16
square units. What is the volume of the cube?
\newline
____ cubic units
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David needs to buy a bathroom mirror that is
2
2
2
feet wide and
2
2
2
feet long. If the mirror sells for
$
1.00
\$1.00
$1.00
per square foot, what will the total cost of the mirror be?
\newline
$
\$
$
_____
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The area of a rectangular price tag is
15
square centimeters
15 \, \text{square centimeters}
15
square centimeters
. It is
3
centimeters
3 \, \text{centimeters}
3
centimeters
tall. How wide is it?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
centimeters
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A rectangular concrete patio has a perimeter of
36
meters
36\,\text{meters}
36
meters
. Its area is
80
square meters
80\,\text{square meters}
80
square meters
. What are the dimensions of the patio?
\newline
_
_
_
_
\_\_\_\_
____
meters by
_
_
_
_
\_\_\_\_
____
meters
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Each side of a square classroom is
5
meters
5\,\text{meters}
5
meters
long. The school wants to replace the carpet in the classroom with new carpet that costs
$
65.00
\$65.00
$65.00
per square meter. How much will the new carpet cost?
\newline
$
_
_
_
\$\_\_\_
$___
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The surface of an air hockey table has an area of
40
40
40
square feet and a perimeter of
28
28
28
feet. What are the dimensions of the air hockey table?
\newline
_
_
_
\_\_\_
___
feet by
_
_
_
\_\_\_
___
feet
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A farmer needs to build a goat pen. The pen will be
6
yards
6\,\text{yards}
6
yards
wide and
9
yards
9\,\text{yards}
9
yards
long. The fencing material costs
$
4.00
\$4.00
$4.00
per yard. How much will it cost to buy enough fencing material to build the goat pen?
\newline
$
\$
$
_____
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A rectangular goat pen has an area of
24
square meters
24\,\text{square meters}
24
square meters
and a perimeter of
20
meters
20\,\text{meters}
20
meters
. What are the dimensions of the pen?
\newline
_
_
_
_
\_\_\_\_
____
meters by
_
_
_
_
\_\_\_\_
____
meters
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The perimeter of a rectangular living room is
34
34
34
meters. The area is
72
72
72
square meters. What are the dimensions of the living room?
\newline
_
_
_
\_\_\_
___
meters by
_
_
_
\_\_\_
___
meters
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The area of a rectangular restaurant kitchen is
70
square meters
70\,\text{square meters}
70
square meters
. The perimeter is
34
meters
34\,\text{meters}
34
meters
. What are the dimensions of the kitchen?
\newline
_
_
_
_
\_\_\_\_
____
meters by
_
_
_
_
\_\_\_\_
____
meters
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Measurements of a room are
7
m
50
cm
7\text{m}50\text{cm}
7
m
50
cm
,
6
m
8
c
m
6\text{m}8{cm}
6
m
8
c
m
3
m
75
cm
3\text{m}75\text{cm}
3
m
75
cm
. Find the length of the longest rod that can measure all the three dimensions of the room.
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Measurements of a room are
7
m
50
c
m
,
6
m
&
7\mathrm{~m} 50 \mathrm{~cm}, 6 \mathrm{~m} \&
7
m
50
cm
,
6
m
&
3
m
75
c
m
3 \mathrm{~m} 75 \mathrm{~cm}
3
m
75
cm
. Find the length of the longest rod that can measure all the three dimensions of the room.
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Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is
22
1
4
cm
22\frac{1}{4}\,\text{cm}
22
4
1
cm
tall. It has a rectangular shape and an area of
890
cm
2
890\,\text{cm}^2
890
cm
2
.
\newline
How wide across is Keala's book cover?
\newline
□
cm
\square \,\text{cm}
□
cm
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Japhet is making small rectangular tiles for a mosaic. Each tile has an area of
7
cm
2
7\,\text{cm}^2
7
cm
2
and is
1
1
4
cm
1\frac{1}{4}\,\text{cm}
1
4
1
cm
wide.
\newline
How long is each tile?
\newline
□
cm
\square \,\text{cm}
□
cm
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A sumo wrestling ring is circular and has a circumference of
4.6
π
4.6 \pi
4.6
π
meters.
\newline
What is the area
A
A
A
of the sumo wrestling ring in square meters? Give your answer in terms of
π
\pi
π
.
\newline
A
=
□
A=\square
A
=
□
m
2
\mathrm{m}^{2}
m
2
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An open-topped glass aquarium with a square base is designed to hold
13
13
13
.
5
5
5
cubic feet of water. What is the minimum exterior surface area of the aquarium?
\newline
square feet
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An open-topped glass aquarium with a square base is designed to hold
4
4
4
cubic feet of water. What is the minimum exterior surface area of the aquarium?
\newline
square feet
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An open-topped glass aquarium with a square base is designed to hold
32
32
32
cubic feet of water. What is the minimum possible exterior surface area of the aquarium?
\newline
square feet
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Find the dimensions of a rectangular lawn whose perimeter is
100
100
100
feet and whose area is
600
600
600
square feet
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Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of
15
1
5
m
2
15\frac{1}{5}\,\text{m}^2
15
5
1
m
2
. Gabriel wants it to be
7
3
4
7\frac{3}{4}
7
4
3
long. How wide does the planter box need to be?
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Four glass balls, each with a
2
2
2
.
5
5
5
inch radius, are placed in a box. If the remaining space is to be filled with cotton for padding, how much cotton is needed? Use
3
3
3
.
14
14
14
for
π
\pi
π
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A rectangle has a perimeter of
32
cm
32\,\text{cm}
32
cm
. The length is
6
cm
6\,\text{cm}
6
cm
longer than the width. What is the length?
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Nisha likes to make small rectangular paintings of cats. One of her paintings has an area of
33
cm
2
33\,\text{cm}^2
33
cm
2
and a width of
7
1
2
cm
7 \frac{1}{2}\,\text{cm}
7
2
1
cm
. What is the height of this painting?
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A movie poster is
2
feet
2\,\text{feet}
2
feet
wide and
4
feet
4\,\text{feet}
4
feet
tall. A frame shop charges
$
1.60
\$1.60
$1.60
per foot for a black metal frame. How much would it cost to buy a black metal frame for the movie poster?
\newline
$
\$
$
_____
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A rectangular parking lot is
38
meters
38\,\text{meters}
38
meters
wide and
117
meters
117\,\text{meters}
117
meters
long. What is its perimeter?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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The area of a square market is
25
square meters
25\,\text{square meters}
25
square meters
. How long is each side of the market?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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The area of a square piece of construction paper is
100
square inches
100\,\text{square inches}
100
square inches
. How long is each side of the piece of paper?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
inches
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The perimeter of a rectangular dining room is
22
22
22
meters. The area is
24
24
24
square meters. What are the dimensions of the dining room?
\newline
_
_
_
\_\_\_
___
meters by
_
_
_
\_\_\_
___
meters
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A map of the world has a perimeter of
20
20
20
feet. Its area is
21
21
21
square feet. What are the dimensions of the map?
\newline
_
_
_
\_\_\_
___
feet by
_
_
_
\_\_\_
___
feet
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A rectangular sheet of metal measures
8
8
8
inches by
10
10
10
inches. The metal is worth
$
2.15
\$2.15
$2.15
per square inch. How much is the sheet of metal worth?
\newline
$
\$
$
_____
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A rectangular painting is
6
6
6
feet wide and
6
6
6
feet high. What is its area?
\newline
_
_
_
_
\_\_\_\_
____
square feet
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A rectangular sticker has a perimeter of
26
26
26
centimeters. Its area is
36
36
36
square centimeters. What are the dimensions of the sticker?
\newline
_
_
_
\_\_\_
___
centimeters by
_
_
_
\_\_\_
___
centimeters
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A rectangular red sticker has an area of
18
square millimeters
18 \, \text{square millimeters}
18
square millimeters
and a perimeter of
18
millimeters
18 \, \text{millimeters}
18
millimeters
. What are the dimensions of the sticker?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
millimeters by
_
_
_
_
_
\_\_\_\_\_
_____
millimeters
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An envelope has an area of
50
50
50
square inches and a perimeter of
30
30
30
inches. What are the dimensions of the envelope?
\newline
_
_
_
\_\_\_
___
inches by
_
_
_
\_\_\_
___
inches
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A rectangular sticker has an area of
28
square centimeters
28\,\text{square centimeters}
28
square centimeters
and a perimeter of
22
centimeters
22\,\text{centimeters}
22
centimeters
. What are the dimensions of the sticker?
\newline
_
_
_
_
\_\_\_\_
____
centimeters by
_
_
_
_
\_\_\_\_
____
centimeters
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The area of a square name tag is
25
square centimeters
25\,\text{square centimeters}
25
square centimeters
. How long is each side?
\newline
_
_
_
_
\_\_\_\_
____
centimeters
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A poster has a perimeter of
16
16
16
feet and an area of
15
15
15
square feet. What are the dimensions of the poster?
\newline
_
_
_
_
\_\_\_\_
____
feet by
_
_
_
_
\_\_\_\_
____
feet
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Each side of a square painting is
3
meters
3\,\text{meters}
3
meters
long. What is the painting's perimeter?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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