1) Firstly, we'll need to find the length of all legs. We'll use the distance formula derived from the Pythagorean Theorem
![\begin{gathered} d_(SA)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d_(SA)=\sqrt[]{(6-1)^2+(-6+6)^2}=5 \\ d_(AU)=\sqrt[]{(3-6)^2+(-2+6)^2}=5 \\ d_(SU)=\sqrt[]{(3-1)^2+(-2+6)^2}=2\sqrt[]{5} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/1jhp5xa02r1ewrn8gbwp04cp50m7gy9yee.png)
Since an isosceles triangle has at least 2 congruent sides then this is an Isosceles Triangle.
2) The Perimeter (2P) is the sum of all sides' length of a polygon. Hence
![\begin{gathered} 2P\text{ =5+5+2}\sqrt[]{5} \\ 2P=10+2\sqrt[]{5} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/thuht6bsiueplzogyd3sybag4zcjo88fim.png)
3) So the answer is Isosceles Triangle and 2P =10+2√5