Solved Examples and Worksheet for Finding an Unknown Dimension of a Polygon

Q1Find the value of h in the given polygon if its perimeter is 35 ft.


A. 9 ft
B. 18 ft
C. 10 ft
D. 11 ft

Solutions
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Step: 1
Perimeter of a given polygon = 35 ft. Perimeter of a polygon is the sum of all the side lengths of the polygon.
Step: 2
Given side lengths are 8 ft, 11 ft, 6 ft and h. Here, we should find one missing side length.
Step: 3
The missing side length is h ft.
Step: 4
Add all the known side lengths of the given polygon because perimeter is given.
Step: 5
8 ft + 11 ft + 6 ft = 25 ft.
  [Add.]
Step: 6
Now, subtract 25 ft from the perimeter of 35 ft to know the missing side length.
Step: 7
The missing side length 'h' = 35 ft - 25 ft = 10 ft.
Step: 8
Therefore, h = 10 ft. It means that the length of the missing side is 10 ft.
Correct Answer is :   10 ft
Q2Find the value of h in the given polygon if its perimeter is 31 in.


A. 14 in
B. 12 in
C. 13 in
D. 11 in

Solutions
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Step: 1
Perimeter of a given polygon = 31 in. Perimeter of a polygon is the sum of all the side lengths of the polygon.
Step: 2
Given side lengths are 4 in, 9 in, 7 in and c. Here, we should find one missing side length.
Step: 3
The missing side length is c in.
Step: 4
Add all the known side lengths of the given polygon because perimeter is given.
Step: 5
4 in + 9 in + 7 in = 20 in.
  [Add.]
Step: 6
Now, subtract 20 in from the perimeter of 31 in to know the missing side length.
Step: 7
The missing side length 'c' = 31 in - 20 in = 11 in.
Step: 8
Therefore, c = 11 in. It means that the length of the missing side is 11 in.
Correct Answer is :   11 in
Q3Find the value of d.


A. 10 in
B. 9 in
C. 8 in
D. 7 in

Solutions
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Step: 1
Perimeter of a given polygon = 29 in. Perimeter of a polygon is the sum of all the side lengths of the polygon.
Step: 2
Given side lengths are 9 in, 2 in, 9 in and d. Here, we should find one missing side length.
Step: 3
The missing side length is d in.
Step: 4
Add all the known side lengths of the given polygon because perimeter is given.
Step: 5
9 in + 2 in + 9 in = 20 in.
  [Add.]
Step: 6
Now, subtract 20 in from the perimeter of 29 in to know the missing side length
Step: 7
The missing side length d = 29 in - 20 in = 9 in.
Step: 8
Therefore, d = 9 in. It means that the length of the missing side is 9 in.
Correct Answer is :   9 in
Q4Find the value of d, if perimeter is 30 yd.


A. 12 yd
B. 11 yd
C. 14 yd
D. 13 yd

Solutions
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Step: 1
Perimeter of a given polygon = 30 yd. Perimeter of a polygon is the sum of all the side lengths of the polygon.
Step: 2
Given side lengths are 12 yd, 5 yd, and d. Here, we should find one missing side length.
Step: 3
The missing side length is d yd.
Step: 4
Add all the known side lengths of the given polygon because perimeter is given.
Step: 5
12 yd + 5 yd = 17 yd.
  [Add.]
Step: 6
Now, subtract 17 yd from the perimeter of 30 yd to know the missing side length.
Step: 7
The missing side length d = 30 yd - 17 yd = 13 yd.
Step: 8
Therefore, d = 13 yd. It means that the length of the missing side is 13 yd.
Correct Answer is :   13 yd
Q5Find the value of s.

A. 7 ft
B. 5 ft
C. 8 ft
D. 6 ft

Solutions
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Step: 1
Perimeter of a given polygon = 25 ft. Perimeter of a polygon is the sum of all the side lengths of the polygon.
Step: 2
Given side lengths are 6 ft, 6 ft, 4 ft, 4 ft and s. Here, we should find one missing side length.
Step: 3
The missing side length is s ft.
Step: 4
Add all the known side lengths of the given polygon because perimeter is given.
Step: 5
6 ft + 6 ft + 4 ft + 4 ft = 20 ft.
  [Add.]
Step: 6
Now, subtract 20 ft from the perimeter of 25 ft to know the missing side length.
Step: 7
The missing side length s = 25 ft - 20 ft = 5 ft.
Step: 8
Therefore, s = 5 ft. It means that the length of the missing side is 5 ft.
Correct Answer is :   5 ft
Q6Find the value of s, if the perimeter of the given shape is 26 in.


A. 14 in
B. 8 in
C. 11 in
D. 7 in

Solutions
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Step: 1
Perimeter of a given shape = 26 in. Perimeter of a shape is the sum of all the side lengths of the shape.
Step: 2
Given side lengths are 6 in, 7 in, 5 in, and s. Here, we should find one missing side length.
Step: 3
The missing side length is s in.
Step: 4
Add all the known side lengths of the given shape because perimeter is given.
Step: 5
6 in + 7 in + 5 in = 18 in.
  [Add.]
Step: 6
Now, subtract 18 in from the perimeter of 26 in to know the missing side length.
Step: 7
The missing side length s = 26 in - 18 in = 8 in.
Step: 8
Therefore, s = 8 in. It means that the length of the missing side is 8 in.
Correct Answer is :   8 in
Q7Find the value of q.


A. 4 ft
B. 3 ft
C. 2 ft
D. 1 ft

Solutions
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Step: 1
Perimeter of a given polygon = 25 ft. Perimeter of a polygon is the sum of all the side lengths of the polygon.
Step: 2
Given side lengths are 9 ft, 6 ft, 2 ft, 3 ft, 3 ft, and q. Here, we should find one missing side length.
Step: 3
The missing side length is q ft.
Step: 4
Add all the known side lengths of the given polygon because perimeter is given.
Step: 5
9 ft + 6 ft + 2 ft + 3 ft + 3 ft = 23 ft.
  [Add.]
Step: 6
Now, subtract 23 ft from the perimeter of 25 ft to know the missing side length.
Step: 7
The missing side length q = 25 ft - 23 ft = 2 ft.
Step: 8
Therefore, q = 2 ft. It means that the length of the missing side is 2 ft.
Correct Answer is :   2 ft
Q8Sophia's uncle gifted a painting on her birth day. The measurements of the painting are shown below. Find the missing side length of the painting.


A. 5 ft
B. 6 ft
C. 2 ft
D. 3 ft

Solutions
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Step: 1
Perimeter of the given painting = 22 ft. Perimeter of a polygon is the sum of all the side lengths of the polygon.
Step: 2
Given side lengths are 5 ft, 6 ft, 6 ft, and s. Here, we should find one missing side length.
Step: 3
The missing side length is s ft.
Step: 4
Add all the known side lengths of the given polygon because perimeter is given.
Step: 5
5 ft + 6 ft + 6 ft = 17 ft.
  [Add.]
Step: 6
Now, subtract 17 ft from the perimeter of 22 ft to know the missing side length.
Step: 7
The missing side length s = 22 ft - 17 ft = 5 ft.
Step: 8
Therefore, s = 5 ft. It means that the length of the missing side of the painting is 5 ft.
Correct Answer is :   5 ft
Q9Jim wants to pack a gift box with a piece of gift paper. The measurements of the gift paper are shown below. Find the missing side length of the gift paper.


A. 6 in
B. 8 in
C. 4 in
D. 5 in

Solutions
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Step: 1
Perimeter of the given piece of gift paper = 34 in. Perimeter of a polygon is the sum of all the side lengths of the polygon.
Step: 2
Given side lengths are 9 in, 5 in, 5 in, 9 in and z. Here, we should find one missing side length.
Step: 3
The missing side length is z in.
Step: 4
Add all the known side lengths of the given piece of gift paper because perimeter is given.
Step: 5
9in + 5 in + 9 in + 5 in = 28 in.
  [Add.]
Step: 6
Now, subtract 28 in from the perimeter of 34 in to know the missing side length.
Step: 7
The missing side length z = 34 in - 28 in = 6 in.
Step: 8
Therefore, z = 6 in. It means that the length of the missing side of the given piece of gift paper is 6 in.
Correct Answer is :   6 in
Q10Alexandra bought a pizza and she has cut in into 8 equal pieces. Measurements of each piece are shown below. Find the missing measurement.


A. 3 in
B. 1 in
C. 4 in
D. 2 in

Solutions
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Step: 1
Perimeter of the given shape = 12 in. Perimeter of a shape is the sum of all the side lengths of the shape.
Step: 2
Given side lengths are 5 ft, 5 ft, and x. Here, we should find one missing side length.
Step: 3
The missing side length is x in.
Step: 4
Add all the known side lengths of the given shape because perimeter is given.
Step: 5
5 in + 5 in = 10 in.
  [Add.]
Step: 6
Now, subtract 10 in from the perimeter of 12 in to know the missing side length.
Step: 7
The missing side length x = 12 in - 10 in = 2 in.
Step: 8
Therefore, x = 2 in. It means that the length of the missing side is 2 in.
Correct Answer is :   2 in

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