Question

find the perimeter of the trapezoid with these vertices. (-2, -2), (-5, -2), (6, -5), (-5, -5) give an exact answer (not a decimal approximation). simplify your answer as much as possible. perimeter:

Explanation:

Step1: Calculate the length of the first side

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for two points \((x_1,y_1)\) and \((x_2,y_2)\).
For points \((-2,-2)\) and \((-5,-2)\):
\(d_1=\sqrt{(-5 - (-2))^2+(-2-(-2))^2}=\sqrt{(-3)^2 + 0^2}=3\)

Step2: Calculate the length of the second side

For points \((-5,-2)\) and \((-5,-5)\):
\(d_2=\sqrt{(-5-(-5))^2+(-5 - (-2))^2}=\sqrt{0^2+(-3)^2}=3\)

Step3: Calculate the length of the third side

For points \((-5,-5)\) and \((6,-5)\):
\(d_3=\sqrt{(6-(-5))^2+(-5-(-5))^2}=\sqrt{11^2+0^2}=11\)

Step4: Calculate the length of the fourth side

For points \((6,-5)\) and \((-2,-2)\):
\(d_4=\sqrt{(-2 - 6)^2+(-2-(-5))^2}=\sqrt{(-8)^2+3^2}=\sqrt{64 + 9}=\sqrt{73}\)

Step5: Calculate the perimeter

The perimeter \(P=d_1 + d_2+d_3+d_4\)
\(P=3 + 3+11+\sqrt{73}=17+\sqrt{73}\)

Answer:

\(17+\sqrt{73}\)