Question

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

Answer 1

46.05

Explanation:

Answer 2

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,

`AB=√((-7.42-0)^2+(2.42-7.88)^2)=√(84.868)=9.2124`

The length of side BC is,

`AB=√((7.42-0)^2+(2.42-7.88)^2)=√(84.868)=9.2124`

The length of side CD is,

`CD=√((4.605-7.42)^2+(-6.35-2.42)^2)=√(84.8371)=9.211`

The length of DE is,

`DE=9.21`

The length of AE is,

`CD=√((4.605-7.42)^2+(-6.35-2.42)^2)=√(84.8371)=9.211`

The perimeter of the pentagon is,

`Perimeter=9.2124+9.2124+9.211+9.211+9.21=46.0568`

Hence, the perimeter of the pantagon is 46.0568.