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The United States Pentagon building is modeled on the coordinate plane as regular pentagon ABThe vertices of the pentagon are 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) what is the approximate perimeter in feet of the us pentagon building

The United States Pentagon Building Is Modeled On The Coordinate Plane As Regular Pentagon ABThe Vertices Of The Pentagon Are A742242 B0788C742242D4605635 And E class=

Sagot :

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.

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