The given figure is a triangle.
Let points be P(-5,3), Q(0,-1) and C(4,4)
Using coordinate geometry we can determine the area by:
Area = Mod ([tex]\frac{Px * (Qy - Ry) + Qx * (Ry - Py) + Rx (Py - Qy)}{2}[/tex])
Px, Qx, Rx refers to x coordinates of point P, Q and R, respectively
Py, Qy, Ry refers to y coordinates of point P, Q and R, respectively
Substituting the values in the area formula:
Area = Mod ([tex]\frac{(-5)*(-1-4) + 0*(4-3) + 4* (3-(-1))}{2}[/tex])
⇒ Area = Mod ([tex]\frac{-5*-5 + 0 + 4 * 4}{2}[/tex]
⇒ Area = Mod ([tex]\frac{41}{2}[/tex])
⇒ Area = 20.5 sq. units
