To find the area of the parallelogram apply the formula: \(\displaystyle A=base\times height\)

Since, the paralleogram has a base of \(\displaystyle 5\) and a height of \(\displaystyle 4\) the solution is:
\(\displaystyle A=5\times4=20\)

In order to find the correct perimeter of the parallelogram apply the formula: \(\displaystyle P=2(a+b)\), where \(\displaystyle a=\) the length of one of the diagonal sides and \(\displaystyle b=\) the length of the base. 

In order to find the length of side \(\displaystyle a\), apply the formula: \(\displaystyle a^2+b^2=C^2\). By drawing an altitude from point \(\displaystyle (4,4)\) to \(\displaystyle (4,0)\), a right triangle is formed with a base that has a length of \(\displaystyle 2\) and a height of \(\displaystyle 4\).

Thus, the solution is:
\(\displaystyle a^2 +b^2=c^2\)
\(\displaystyle 2^2+4^2=\) length of side \(\displaystyle a^2\)
\(\displaystyle 4+16=20\)
\(\displaystyle a^2=20\)
\(\displaystyle a=\sqrt{20}\)

Therefore, 

\(\displaystyle P=2(\sqrt{20}+b)\)
\(\displaystyle b=5\)
\(\displaystyle P=2(\sqrt{20}+5)\)

In order to identify the coordinate points for this parallelogram, notice that there must be two different pairs of coordinates with the same \(\displaystyle y\) values. 

Thus, the parallelogram has coordinate points: \(\displaystyle (-2,-1), (-1,2), (3,2), (2,-1)\)

To find the area of the parallelogram that is shown, apply the formula: \(\displaystyle A=base\times height\)
Since the parallelogram has a base of \(\displaystyle 4\) and a height of \(\displaystyle 3\) the solution is:
\(\displaystyle A=4\times 3=12\)

In order to find the perimeter of the parallelogram apply the formula: \(\displaystyle P=2(a+b)\), where \(\displaystyle a=\) the length of one diagonal side and \(\displaystyle b=\) the length of one base. 

In this problem, \(\displaystyle a=\sqrt{10}\) and \(\displaystyle b= 4\).
Thus, the correct answer is: \(\displaystyle P=2(\sqrt{10}+4)\)

In order to identify the coordinate points for this parallelogram, notice that there must be two different pairs of coordinates with the same \(\displaystyle y\) values. 

Thus, the correct set of coordinates is: 
\(\displaystyle (2,0), (4,4), (7,0), (9,4)\)

Plot the points on a coordinate axis. Once it's graphed, you can see that there are two pairs of congruent, or equal, sides. The shape that best fits these characteristics is a rectangle.

In order to find the area of rectangle \(\displaystyle \small ABCD\) apply the formula: \(\displaystyle \small A=width\times length\)

Since rectangle \(\displaystyle \small ABCD\) has a width of \(\displaystyle \small 7\) and a length of \(\displaystyle \small 4\) the solution is:

\(\displaystyle \small A=7\times4=28\) square units

To find the perimeter of rectangle \(\displaystyle \small ABCD\), apply the formula: \(\displaystyle \small p=2(width)+2(length)\)

Thus, the solution is:

\(\displaystyle \small p=2(7)+2(4)\)
\(\displaystyle \small p=14+8\)
\(\displaystyle \small p=22\)

The area of rectangle \(\displaystyle ABCD\) can be found by multiplying the width and length of the rectangle. 

To find the length of the rectangle compare the x values of two of the coordinates:

Since \(\displaystyle A(-2,2), C(2,4)\) the length is \(\displaystyle 2-(-2)=4\).

To  find the width of the rectangle we need to look at the y coordinates of two of the points.

Since \(\displaystyle A(-2,2), C(2,4)\) the width is \(\displaystyle 4-2=2\).

The solution is:

\(\displaystyle A=w\times l\)
\(\displaystyle A=4\times2=8\)