Question 1081939
.
The area is 2 square units.



Your area is a quadrilateral (actually, a square around the origin of the coordinate system) restricted by the lines. 



{{{graph( 330, 330, -3.5, 3.5, -3.5, 3.5,
          1-abs(x), -(1-abs(x))
)}}}


Plot y = 1 - |x|  (red) and y = -(1 - |x|) (green)