Solution:
Given the parallelogram below:
According to the properties of a parallelogram, the opposite sides are parallel and equal in dimensions.
Thus,
[tex]\begin{gathered} AD=BC \\ and \\ AB=DC \end{gathered}[/tex]
A) Height of the parallelogram:
The length BE is the height of the parallelogram, which is evaluated using the Pythagorean theorem.
According to the Pythagorean theorem,
[tex]\begin{gathered} (BC)^2=(BE)^2+(EC)^2 \\ \end{gathered}[/tex]
Where
[tex]\begin{gathered} BC=9 \\ BE=h \\ EC\text{ is unknown} \end{gathered}[/tex]
To evaluate h, we need to determine the value of EC.
Recall that
[tex]\begin{gathered} AB=DC \\ where \\ DC=DE+EC \\ \Rightarrow AB=DE+EC \end{gathered}[/tex]
Thus, we have
[tex]\begin{gathered} 9=6+EC \\ subtract\text{ 6 from both sides of the equation} \\ 9-6=6-6+EC \\ \Rightarrow EC=3\text{ in.} \end{gathered}[/tex]
We can now determine the value of h.
From the Pythagorean theorem,
[tex]undefined[/tex]
