This math topic focuses on finding the length of a side of a partially shaded rectangle, given the total area of the rectangle and the area of the shaded part. It introduces students to logical reasoning with geometrical shapes, involving area calculation and proportion. The problems are structured to identify the relationship between the total and partial areas to determine the dimensions of subsets of shapes, reinforcing foundational concepts in area and perimeter calculations within practical contexts. This prepares students for more complex geometry and spatial reasoning tasks.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Area of a Part Rectangle - Areas and Full Side Length to Part Side Length Worksheet

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Area of a Part Rectangle - Areas and Full Side Length to Part Side Length
1
The full rectangle's area is 8. The area that is filled in is 4. What is the width of the part side?
An svg image showing a math problem
a
3
b
2
c
6
d
1
e
7
f
8
2
The full rectangle's area is 40. The area that is filled in is 20. What is the width of the part side?
An svg image showing a math problem
a
10
b
6
c
4
d
12
e
3
f
7
3
The full rectangle's area is 96. The area that is filled in is 72. What is the width of the part side?
An svg image showing a math problem
a
18
b
10
c
1
d
9
e
4
f
13
4
The full rectangle's area is 60. The area that is filled in is 30. What is the width of the part side?
An svg image showing a math problem
a
12
b
1
c
13
d
3
e
2
f
5
5
The full rectangle's area is 8. The area that is filled in is 4. What is the width of the part side?
An svg image showing a math problem
a
11
b
7
c
2
d
10
e
4
f
8
6
The full rectangle's area is 48. The area that is filled in is 24. What is the width of the part side?
An svg image showing a math problem
a
9
b
4
c
6
d
10
e
12
f
8
7
The full rectangle's area is 70. The area that is filled in is 56. What is the width of the part side?
An svg image showing a math problem
a
5
b
6
c
8
d
7
e
2
f
13
8
The full rectangle's area is 32. The area that is filled in is 16. What is the width of the part side?
An svg image showing a math problem
a
1
b
11
c
9
d
10
e
2
f
4