Answer:
[tex]12\sqrt{2}[/tex]
Step-by-step explanation:
The easiest way personally for me is to graph it out, but you can also calculate it out.
A = (1,1)
B = (4,4)
C = (7,1)
D = (4,-2)
Attached is the distance formula. Use it to your advantage. Find the slope for all the points:
Point A to B: [tex]\sqrt{(4-1)^{2}+(4-1)^{2} }[/tex] = [tex]\sqrt{9+9 }[/tex]
Point B to C: [tex]\sqrt{(7-4)^{2}+(1-4)^{2} }[/tex] = [tex]\sqrt{9+9}[/tex]
Point C to D: [tex]\sqrt{(4-7)^{2}+(-2-1)^{2} }[/tex] = [tex]\sqrt{9+9}[/tex]
Point D to A: [tex]\sqrt{(4-1)^{2}+(-2-1)^{2} }[/tex] = [tex]\sqrt{9+9}[/tex]
When you add all of it up, it will equal to [tex]\sqrt{18} + \sqrt{18} + \sqrt{18} + \sqrt{18} = 4\sqrt{18[/tex] and which simplifies to [tex]12\sqrt{2}[/tex].
