Question

graph the polygon and then find the area and perimeter

Answer 1

Graphing the points given and the corresponding sides, we have:

We can see that the distance between P and Q and the distance between R and S is 7 units (they have the same y-coordinate, so the distance is the difference in x-coordinates).

Also, the vertical distance between Q and R and the vertical distance between P and S is 9 units (just the difference in y-coordinates).

Since this figure is a parallelogram (opposite sides are parallel), we can calculate the area as the base PQ times the height (the height is 9 units):

$\text{Area}=7\cdot9=63$

The length of segments QR and PS can be calculated using Pythagorean Theorem, with the difference in x-coordinates being 3 units and the difference in y-coordinates being 9 units:

$\begin{gathered} QR^2=3^2+9^2 \\ QR^2=9+81 \\ QR^2=90 \\ QR=9.49 \end{gathered}$

So the perimeter of this parallelogram is:

$\text{Perimeter}=7+9.49+7+9.49=32.98$