It can be shown that if A and B are vectors giving two non-parallel sides of a parallelogram, then |A x B| is the area of the parallelogram. Since we can always think of a triangle as half of a parallelogram, the area of a triangle, with sides given by vectors A and B, is 1/2 |A x B|.
HOWEVER, here, OP, OR, and OS are NOT the sides of this triangle so NONE of the formulas you give are correct. The vector PR= OP- OR is a side of the triangle.
