A parallelogram must have two sets of congruent/parallel opposite sides. This parallelogram must have two sides with a measurement of \(\displaystyle 16\textup{mm}\) and two base sides each with a length of \(\displaystyle 24\textup{mm}\). In this question, you are provided with the information that the parallelogram has a base of \(\displaystyle 24\textup{mm}\) and a total perimeter of \(\displaystyle 80\textup{mm}\). Thus, work backwards using the perimeter formula in order to find the length of one missing side that is adjacent to the base.

\(\displaystyle \textup{Perimeter}=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the measurements of adjacent sides. 

Thus, the solution is:

\(\displaystyle 80=2(24+b)\)

\(\displaystyle 80=48+2b\)

\(\displaystyle 2b=80-48=32\)

\(\displaystyle b=\frac{32}{2}=16\)

A parallelogram must have two sets of congruent/parallel opposite sides. This parallelogram must have two sides with a measurement of \(\displaystyle 25\) and two base sides each with a length of \(\displaystyle 16\). In this question, you are given the information that the parallelogram has a base of \(\displaystyle 16\) and a total perimeter of \(\displaystyle 82\). Thus, work backwards using the perimeter formula in order to find the sum of the two adjacent sides to the base.

\(\displaystyle \textup{Perimeter}=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the measurements of adjacent sides. 

Thus, the solution is:

\(\displaystyle 82=2(16+b)\)

\(\displaystyle 82=32+2b\)

\(\displaystyle 2b=82-32=50\)

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of \(\displaystyle 45\textup{mm}\) and two base sides each with a length of \(\displaystyle 55\textup{mm}\). To find the perimeter of the parallelogram apply the formula: 

\(\displaystyle \textup{Perimeter}=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the measurements of adjacent sides. 

Thus, the solution is:

\(\displaystyle p=2(55+45)\)

\(\displaystyle p=2(100)\)

\(\displaystyle p=200\)

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of \(\displaystyle 136\textup{ inches}\) and two base sides each with a length of \(\displaystyle 140\textup{ inches}\). However, to solve this problem you must first convert the provided perimeter measurement from feet to inches. Since an inch is \(\displaystyle \frac{1}{12}\) of \(\displaystyle 1\) foot, \(\displaystyle 46\) feet is equal to\(\displaystyle 46\times12=552\) inches.

Now, you can work backwards using the formula: 

\(\displaystyle \textup{Perimeter}=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the measurements of adjacent sides. 

Thus, the solution is:

\(\displaystyle 552=2(140+b)\)

\(\displaystyle 552=280+2b\)

\(\displaystyle 2b=552-280=272\) 

\(\displaystyle b=\frac{272}{2}=136\)

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of \(\displaystyle 16\) and two base sides each with a length of \(\displaystyle 18.\) Since the perimeter and one base length is provided in the question, work backwards using the perimeter formula:

\(\displaystyle \textup{Perimeter}=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the measurements of adjacent sides. 

Thus, the solution is:

\(\displaystyle 68=2(18+b)\)

\(\displaystyle 68=36+2b\)

\(\displaystyle 2b=68-36=32\)

\(\displaystyle b=\frac{32}{2}=16\)

A parallelogram must have two sets of congruent/parallel opposite sides. This parallelogram must have two sides with a measurement of \(\displaystyle 14\) and two base sides each with a length of \(\displaystyle 22\). In this question, you are provided with the information that the parallelogram has a base of \(\displaystyle 22\) and a total perimeter of \(\displaystyle 72\). Thus, work backwards using the perimeter formula in order to find the sum of the two adjacent sides to the base.

\(\displaystyle \textup{Perimeter}=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the measurements of adjacent sides. 

Thus, the solution is:

\(\displaystyle 72=2(22+b)\)

\(\displaystyle 72=44+2b\)

\(\displaystyle 2b=72-44=28\)

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of \(\displaystyle 18\) and two base sides each with a length of \(\displaystyle 28.\) To find the perimeter of the parallelogram apply the formula: 

\(\displaystyle \textup{Perimeter}=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the measurements of adjacent sides. 

Thus, the solution is:

\(\displaystyle p=2(28+18)\)

\(\displaystyle p=2(46)\)

\(\displaystyle p=92\)

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of \(\displaystyle 74\textup{mm}\) and two base sides each with a length of \(\displaystyle 95\textup{mm}\). To solve for the missing side, work backwards using the perimeter formula: 

\(\displaystyle \textup{Perimeter}=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the measurements of adjacent sides. 

Thus, the solution is:

\(\displaystyle 338=2(95+b)\)

\(\displaystyle 338=190+2b\)

\(\displaystyle 2b=338-190=148\)

\(\displaystyle b=\frac{148}{2}=74\)

We are told that the shape is a quadrilateral and that the sides are equal; beyond that, we do not know what specific kind of kind of quadrilateral it is, outside of the fact that it is a rhombus. The perimeter, the sum of the sides, is \(\displaystyle 16\).

If this shape were a square, the area would also be \(\displaystyle 16\); however, if the interior angles were not all equivalent, the area would be smaller than this.

The relationship cannot be determined.