The image asks to find the perimeter of a polygon given the vertices:

• (3,5)
• (4,2)
• (3,1)
• (-4,-2)

To find the perimeter, we need to calculate the distance between each consecutive pair of points and then add up the distances. The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Step-by-Step Calculation:

1. Distance between (3,5) and (4,2): $d_1 = \sqrt{(4 - 3)^2 + (2 - 5)^2} = \sqrt{1^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}$

2. Distance between (4,2) and (3,1): $d_2 = \sqrt{(3 - 4)^2 + (1 - 2)^2} = \sqrt{(-1)^2 + (-1)^2} = \sqrt{1 + 1} = \sqrt{2}$

3. Distance between (3,1) and (-4,-2): $d_3 = \sqrt{(-4 - 3)^2 + (-2 - 1)^2} = \sqrt{(-7)^2 + (-3)^2} = \sqrt{49 + 9} = \sqrt{58}$

4. Distance between (-4,-2) and (3,5): $d_4 = \sqrt{(3 - (-4))^2 + (5 - (-2))^2} = \sqrt{(3 + 4)^2 + (5 + 2)^2} = \sqrt{7^2 + 7^2} = \sqrt{49 + 49} = \sqrt{98}$

Now, add the distances together to get the perimeter:

$\text{Perimeter} = \sqrt{10} + \sqrt{2} + \sqrt{58} + \sqrt{98}$

You can compute this numerically for the final perimeter value.

Would you like me to calculate the final value for the perimeter or explain any part of this further?