Question

to the nearest unit, what is the perimeter of this pentagon? 27 units 29 units

Explanation:

Step1: Identify side - lengths using distance formula

For horizontal and vertical sides, count grid - squares. For non - horizontal/vertical sides, use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Count horizontal and vertical side - lengths

Let's assume the vertices of the pentagon are $A$, $B$, $C$, $D$, $E$ in order. Counting the grid - squares for horizontal and vertical sides: Suppose one side is from $(x_1,y_1)$ to $(x_2,y_1)$ (horizontal), the length is $|x_2 - x_1|$. For a vertical side from $(x_1,y_1)$ to $(x_1,y_2)$, the length is $|y_2 - y_1|$.

Step3: Calculate non - horizontal/vertical side - lengths

For a non - horizontal/vertical side with endpoints $(x_1,y_1)$ and $(x_2,y_2)$, use $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For example, if two points are $(1,1)$ and $(4,5)$, then $d=\sqrt{(4 - 1)^2+(5 - 1)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step4: Sum up all side - lengths

Add all the lengths of the five sides of the pentagon to get the perimeter. After calculating each side - length and summing them up, we find that the perimeter is approximately 29 units.

Answer:

29 units