Question 946623
A(1,2), B(2,-1), C(-1,-2), D(-2,1) 

first draw a polygon using given vertices:


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(1,2,.12), circle(2,-1,.12),circle(-1,-2,.12), circle(-2,1,.12),

locate(1,2,A(1,2)), locate(2,-1,B(2,-1)),

locate(-1,-2,C(-1,-2)), locate(-2,1,D(-2,1)),

blue(line(1,2,2,-1)), blue(line(1,2,-2,1)),
blue(line(2,-1,-1,-2)), blue(line(-2,1,-1,-2)),
graph( 600, 600, -10, 10, -10, 10, 0)) }}} 


find distance {{{AB},{{{AD},{{{CD}}},{{{BC}:

A(1,2), B(2,-1), C(-1,-2), D(-2,1) 

*[invoke Distance_Formula_for_Coordinate_Plane 1, 2, 2, -1] 

{{{AD}
*[invoke Distance_Formula_for_Coordinate_Plane 1, 2, -2,1] 

{{{CD}}}
*[invoke Distance_Formula_for_Coordinate_Plane -1,-2, -2,1] 

{{{BC}
*[invoke Distance_Formula_for_Coordinate_Plane -1,-2, 2, -1] 


 since all distances same => your polygon is a square and the length of its side is {{{a=3.16227766016838}}}
then the area and perimeter of this polygon will be:

{{{A=a^2}}}

{{{A=(3.16227766016838)^2}}}

{{{A=10}}}

perimeter:
{{{P=4a}}}
{{{P=4*3.16227766016838}}}
{{{P=12.64911064067352}}}
{{{P=12.65}}}