Answer:
Amount of fencing required = 75 yards
Step-by-step explanation:
Distance between the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the formula,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between A(3, 6) and B(3, -2) = [tex]\sqrt{(3-3)^2+(6+2)^2}[/tex]
= 8 yards
Distance between B(3, -2) and C(-7, 4) = [tex]\sqrt{(3+7)^2+(-2-4)^2}[/tex]
= [tex]\sqrt{136}[/tex]
= 11.66 ≈ 12 yards
Distance between C(-7, 4) and D(-7, -2) = [tex]\sqrt{(-7+7)^2+(4+2)^2}[/tex]
= 6 yards
Distance between D(-7, -2) and E(-3, -2) = [tex]\sqrt{(-7+3)^2+(-2+2)^2}[/tex]
= 4 yards
Distance between E(-3, -2) and F(-3, -8) = [tex]\sqrt{(-3+3)^2+(-2+8)^2}[/tex]
= 6 yards
Distance between F(-3, -8) and G(3, -8) = [tex]\sqrt{(-3-3)^2+(-8+8)^2}[/tex]
= 6 yards
Distance between G(3, -8) and H(10, -12) = [tex]\sqrt{(3-10)^2+(-8+12)^2}[/tex]
= [tex]\sqrt{49+16}[/tex]
= [tex]\sqrt{65}[/tex]
= 8.06 ≈ 8 yards
Distance between H(10, -12) and J(10, 6) = [tex]\sqrt{(10-10)^2+(-12-6)^2}[/tex]
= 18 yards
Distance between A(3, 6) and J(10, 6) = [tex]\sqrt{(10-3)^2+(6-6)^2}[/tex]
= 7 yards
Since length of fence required = perimeter of the flat area
Perimeter of the given area = 8 + 12 + 6 + 4 + 6 + 6 + 8 + 18 + 7
= 75 yards
Therefore, amount of fencing required = 75 yards
