Question

find the perimeter of the figure if each unit on the graph measures 1 cm if necessary.
11.3 cm
8.1 cm
11.2 cm
11.4 cm

Explanation:

Step1: Use distance formula

For two - points $(x_1,y_1)$ and $(x_2,y_2)$, $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Calculate side lengths.

Step2: Calculate $EH$

$E(3,-5)$ and $H(1,-3)$, $d_{EH}=\sqrt{(1 - 3)^2+(-3+5)^2}=\sqrt{4 + 4}=2\sqrt{2}$.

Step3: Calculate $HG$

$H(1,-3)$ and $G(3,-1)$, $d_{HG}=\sqrt{(3 - 1)^2+(-1 + 3)^2}=2\sqrt{2}$.

Step4: Calculate $GF$

$G(3,-1)$ and $F(5,-3)$, $d_{GF}=\sqrt{(5 - 3)^2+(-3 + 1)^2}=2\sqrt{2}$.

Step5: Calculate $FE$

$F(5,-3)$ and $E(3,-5)$, $d_{FE}=\sqrt{(3 - 5)^2+(-5 + 3)^2}=2\sqrt{2}$.

Step6: Calculate perimeter

$P=4\times2\sqrt{2}\approx11.3$ cm.

Answer:

11.3 cm