What is the perimeter of a polygon with vertices at (−1, 3) , ​ (−1, 6) ​, (2, 10) , ​ (5, 6) ​​, and ​​ ​ (5, 3) ​? Enter your answer in the box. Do not round any side lengths.​ _ units

check the picture below.

the sides at the bottom there, you can pretty much count their length off the grid.

now, the slanted ones, the red ones, are just twins, so we can just find the length of one, since the other will have the same length.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ -1}} &,&{{ 6}}~) % (c,d) &&(~{{ 2}} &,&{{10}}~) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[2-(-1)]^2+[10-6]^2}\implies d=\sqrt{(2+1)^2+(10-6)^2} \\\\\\ d=\sqrt{3^2+4^2}\implies d=\sqrt{9+16}\implies d=\sqrt{25}\implies d=5[/tex]

so, the perimeter of the polygon, is all its sides added up, so, notice each of the red ones are 5 each, count the others, add them up, and that's the perimeter.