Given,
The coordinates of the vertices of the pentagon is,
A(-7.42,2.42), B(0,7.88), C(7.42,2.42),D(4.605,-6.35), and E(-4.605-6.35)
Required
The approximate perimeter of the pentagon.
The perimeter of the pentagon is calculated as,
The length of side AB is,
[tex]AB=\sqrt{(-7.42-0)^2+(2.42-7.88)^2}=\sqrt{84.868}=9.2124[/tex]The length of side BC is,
[tex]AB=\sqrt{(7.42-0)^2+(2.42-7.88)^2}=\sqrt{84.868}=9.2124[/tex]The length of side CD is,
[tex]CD=\sqrt{(4.605-7.42)^2+(-6.35-2.42)^2}=\sqrt{84.8371}=9.211[/tex]The length of DE is,
[tex]DE=9.21[/tex]The length of AE is,
[tex]CD=\sqrt{(4.605-7.42)^2+(-6.35-2.42)^2}=\sqrt{84.8371}=9.211[/tex]The perimeter of the pentagon is,
[tex]Perimeter=9.2124+9.2124+9.211+9.211+9.21=46.0568[/tex]Hence, the perimeter of the pantagon is 46.0568.