Answer:
24 units
Step-by-step explanation:
The polygon with 5 vertices A (-2,1), B (-2, 4) , C (2, 7), D (6, 4) and E (6, 1).
where A [tex](x_{1} , y_{1}) = (-2, 1)[/tex], B [tex](x_{2} , y_{2}) = (-2, 4)[/tex]
C [tex](x_{3} , y_{3}) = (2, 7)[/tex] , D [tex](x_{4} , y_{4}) = (6, 4)[/tex]
E [tex](x_{5} , y_{5}) = (6, 1)[/tex]
Now using distance formula:
Length of AB = [tex]\sqrt{\left(x_{2}- x_{1}\right)^{2}+ \left (y_{2} -y_{1}\right)^{2}}[/tex]
= [tex]\sqrt{(-2+2)^{2} +(4 - 1)^{2} }[/tex]
= [tex]\sqrt{0^{2} +3^{2} }[/tex]
= [tex]\sqrt{3^{2} } = 3 unit[/tex]
Length of BC = [tex]\sqrt{\left(x_{3}- x_{2}\right)^{2}+ \left (y_{3} -y_{2}\right)^{2}}[/tex]
= [tex]\sqrt{(2- (-2))^{2} +(7 - 4)^{2} }[/tex]
= [tex]\sqrt{4^{2} +3^{2} }[/tex]
=[tex]\sqrt{16 + 9}[/tex]
= [tex]\sqrt{25^{2} } = 5 unit[/tex]
Length of CD = [tex]\sqrt{\left(x_{4}- x_{3}\right)^{2}+ \left (y_{4} -y_{3}\right)^{2}}[/tex]
= [tex]\sqrt{(6-2)^{2} +(4 - 7)^{2} }[/tex]
= [tex]\sqrt{4^{2} +(-3)^{2} }[/tex]
= [tex]\sqrt{16 + 9}[/tex]
= [tex]\sqrt{25} = 5 unit[/tex]
Length of DE = [tex]\sqrt{\left(x_{5}- x_{4}\right)^{2}+ \left (y_{5} -y_{4}\right)^{2}}[/tex]
= [tex]\sqrt{(6 - 6)^{2} +(1 - 4)^{2} }[/tex]
= [tex]\sqrt{0^{2} +(-3)^{2} }[/tex]
= [tex]\sqrt{0 + 9}[/tex]
= 3 unit
Length of EA = [tex]\sqrt{\left(x_{5}- x_{1}\right)^{2}+ \left (y_{5} -y_{1}\right)^{2}}[/tex]
= [tex]\sqrt{(6 - (- 2))^{2} +(1 - 1)^{2} }[/tex]
= [tex]\sqrt{(6 + 2)^{2} +(0)^{2} }[/tex]
= [tex]\sqrt{8^{2} +(0)^{2} }[/tex]
= 8 unit
Perimeter of polygon = Length of (AB + BC + CD + DE + EA)
= (3 + 5 + 5 + 3 + 8)
= 24 units
