Question

what is the perimeter of trapezoid jklm?
√2 + √5 units
2 + √2 + √5 units
9 + 2√2 units
9 + √2 + √5 units

Explanation:

Step1: Calculate the length of \(JK\)

Since \(J(-7,4)\) and \(K(-4,4)\), using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) (or for horizontal line \(y\) - coordinate is same: \(d=\vert x_2 - x_1\vert\)).
\(JK=\vert-4-(-7)\vert=\vert-4 + 7\vert=3\)

Step2: Calculate the length of \(ML\)

Since \(M(-8,3)\) and \(L(-2,3)\), using the distance formula for horizontal line (\(y\) - coordinate is same: \(d=\vert x_2 - x_1\vert\)).
\(ML=\vert-2-(-8)\vert=\vert-2 + 8\vert=6\)

Step3: Calculate the length of \(JM\)

Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \(J(-7,4)\) and \(M(-8,3)\)
\(JM=\sqrt{(-8+7)^2+(3 - 4)^2}=\sqrt{(-1)^2+(-1)^2}=\sqrt{1 + 1}=\sqrt{2}\)

Step4: Calculate the length of \(KL\)

Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \(K(-4,4)\) and \(L(-2,3)\)
\(KL=\sqrt{(-2 + 4)^2+(3 - 4)^2}=\sqrt{(2)^2+(-1)^2}=\sqrt{4+1}=\sqrt{5}\)

Step5: Calculate the perimeter \(P\)

The perimeter of trapezoid \(P = JK+ML+JM+KL\)
\(P=3 + 6+\sqrt{2}+\sqrt{5}=9+\sqrt{2}+\sqrt{5}\)

Answer:

\(9+\sqrt{2}+\sqrt{5}\) units (the fourth option)