Question

pentagon brave has vertices with coordinates, b(-2, -7), r(3, -7), a(4, -3), v(4, 3), and e(-1, 1). find the perimeter of pentagon brave. round your answer to the nearest hundredth. use the keypad to enter the answer in the box provided. the perimeter of pentagon brave is units.

Explanation:

Step1: Calculate the length of \(BR\)

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For \(B(-2,-7)\) and \(R(3,-7)\), \(x_1=-2,y_1 = - 7,x_2=3,y_2=-7\).
\(BR=\sqrt{(3-(-2))^2+(-7 - (-7))^2}=\sqrt{(3 + 2)^2+(0)^2}=\sqrt{25}=5\)

Step2: Calculate the length of \(RA\)

For \(R(3,-7)\) and \(A(4,-3)\), \(x_1 = 3,y_1=-7,x_2=4,y_2=-3\)
\(RA=\sqrt{(4 - 3)^2+(-3-(-7))^2}=\sqrt{1+(4)^2}=\sqrt{1 + 16}=\sqrt{17}\approx4.123\)

Step3: Calculate the length of \(AV\)

For \(A(4,-3)\) and \(V(4,3)\), \(x_1=4,y_1=-3,x_2=4,y_2=3\)
\(AV=\sqrt{(4 - 4)^2+(3-(-3))^2}=\sqrt{0+(6)^2}=6\)

Step4: Calculate the length of \(VE\)

For \(V(4,3)\) and \(E(-1,1)\), \(x_1=4,y_1=3,x_2=-1,y_2=1\)
\(VE=\sqrt{(-1 - 4)^2+(1 - 3)^2}=\sqrt{(-5)^2+(-2)^2}=\sqrt{25 + 4}=\sqrt{29}\approx5.385\)

Step5: Calculate the length of \(EB\)

For \(E(-1,1)\) and \(B(-2,-7)\), \(x_1=-1,y_1=1,x_2=-2,y_2=-7\)
\(EB=\sqrt{(-2-(-1))^2+(-7 - 1)^2}=\sqrt{(-1)^2+(-8)^2}=\sqrt{1+64}=\sqrt{65}\approx8.062\)

Step6: Calculate the perimeter \(P\)

\(P=BR + RA+AV+VE+EB\)
\(P=5+\sqrt{17}+6+\sqrt{29}+\sqrt{65}\)
\(P\approx5 + 4.123+6+5.385+8.062\)
\(P\approx28.57\)

Answer:

\(28.57\)