In counterclockwise order that's
R(2,4), Q(-4,4), U(-4,3), T(2,-3), S(5,-3)
That's a trapezoid, height 7 upper base 6, lower base 9, so average base 15/2 and area 7(15)/2 = 105/2 = 52.5.
Answer: 52.5
The shoelace theorem gives the answer without thinking. We write the list on top of itself shifted and add up the cross produces:
R(2,4), Q(-4,4), U(-4,-3), T(2,-3), S(5,-3)
Q(-4,4), U(-4,-3), T(2,-3), S(5,-3), R(2,4),