the perimeter of any figure, is just all sides summed up
now, sides RU and UT, you can pretty much see how long they are right off the grid, just count the grid units
now SR and ST, just use the distance equation
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) S&({{ -2}}\quad ,&{{ 7}})\quad % (c,d) T&({{2}}\quad ,&{{ 5}})\\\\ S&({{ -2}}\quad ,&{{ 7}})\quad % (c,d) R&({{-1}}\quad ,&{{ 3}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}]()
![\bf ST=√([2-(-2)]^2+(5-7)^2)\implies ST=√((2+2)^2+(5-7)^2) \\\\\\ ST=√((4)^2+(-2)^2)\\\\\\ SR=√([-1-(-2)]^2+[3-7]^2)\implies SR=√((-1+2)^2+(3-7)^2) \\\\\\ SR=√((1)^2+(-4)^2)](https://img.qammunity.org/2018/formulas/mathematics/high-school/zuw2kvgic76beptvu86odta5xedq0uaaq0.png)
sum up all their distances, and that's the perimeter of the shape