Answer:
12.4 units
Step-by-step explanation:
G(-1,3) ; F(2,4) ; E(-1,6); H(-3,3)
[tex]Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\GF=\sqrt{(2-[-1])^{2}+(4-3)^{2}}\\\\=\sqrt{(2+1)^{2}+(1)^{2}}\\\\=\sqrt{(3)^{2}+1}\\\\=\sqrt{9+1}\\\\=\sqrt{10}\\\\=3.2 units[/tex]
[tex]FE=\sqrt{(-1-2)^{2}+(6-4)^{2}}\\\\=\sqrt{(-3)^{2}+(2)^{2}}\\=\sqrt{9+4}\\\\=\sqrt{13}\\\\=3.6 units[/tex]
[tex]EH=\sqrt{(-3+1)^{2}+(3-6)^{2}}\\\\=\sqrt{(-2)^{2}+(-3)^{2}}\\\\=\sqrt{4+9}\\\\=\sqrt{13}\\\\=3.6 units[/tex]
[tex]GH=\sqrt{(-3+1)^{2}+(3-3)^{2}}\\\\=\sqrt{(-2)^{2}+0}\\\\=\sqrt{4}\\\\=2[/tex]
Perimeter = 3.2 + 3.6 + 3.6 + 2 =12.4 units
