Question

what is the perimeter of a polygon with vertices at $(3,2)$, $(3,9)$, $(7,12)$, $(11,9)$, and $(11,2)$? enter your answer in the box. do not round any side lengths. units

Explanation:

Step1: Calculate the length of each side

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) or for vertical/horizontal sides:

• For vertical side \((3,2)\) to \((3,9)\): \(d_1=\vert9 - 2\vert=7\)
• For side \((3,9)\) to \((7,12)\): \(d_2=\sqrt{(7 - 3)^2+(12 - 9)^2}=\sqrt{16 + 9}=\sqrt{25}=5\)
• For side \((7,12)\) to \((11,9)\): \(d_3=\sqrt{(11 - 7)^2+(9 - 12)^2}=\sqrt{16+9}=\sqrt{25}=5\)
• For vertical side \((11,9)\) to \((11,2)\): \(d_4=\vert9 - 2\vert=7\)
• For horizontal side \((11,2)\) to \((3,2)\): \(d_5=\vert11 - 3\vert=8\)

Step2: Sum up all side lengths

\(P=d_1 + d_2 + d_3 + d_4 + d_5=7 + 5+5 + 7+8\)

Answer:

\(32\)