Find the perimeter of the parallelogram with these vertices, \[ (-2,2),(-2,-2),(3,-2),(3,-6) \] Give an exact answer (not a decimal approximation). Simplify your answer as much as possible. Scratch Area (Not

To find the perimeter of the parallelogram defined by the vertices \((-2,2)\), \((-2,-2)\), \((3,-2)\), and \((3,-6)\), we can follow these steps: 1. **Identify the vertices**: The vertices are given as: - \(A = (-2, 2)\) - \(B = (-2, -2)\) - \(C = (3, -2)\) - \(D = (3, -6)\) 2. **Calculate the lengths of the sides**: The perimeter \(P\) of a parallelogram is given by the formula: \[ P = 2(a + b) \] where \(a\) and \(b\) are the lengths of the adjacent sides. - **Length of side \(AB\)**: \[ AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{((-2) - (-2))^2 + ((-2) - 2)^2} = \sqrt{0 + (-4)^2} = \sqrt{16} = 4 \] - **Length of side \(BC\)**: \[ BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} = \sqrt{(3 - (-2))^2 + ((-2) - (-2))^2} = \sqrt{(5)^2 + 0} = \sqrt{25} = 5 \] 3. **Calculate the perimeter**: Now that we have the lengths of the sides: - \(a = AB = 4\) - \(b = BC = 5\) We can substitute these values into the perimeter formula: \[ P = 2(a + b) = 2(4 + 5) = 2(9) = 18 \] Thus, the perimeter of the parallelogram is \(\boxed{18}\).