Chapter 9 - Polar Coordinates; Vectors - 9.3 The Complex Plane; De Moivre's Theorem - 9.3 Assess Your Understanding - Page 595: 71

approximately $40.5$ square units

By definition, the area $K$ of a triangle whose two sides and the included angle are known is given by the formula $K=\frac{ab\cdot sin(C)}{2}.$ Hence, here we have: $K=\dfrac{8\cdot11\cdot \sin(113^\circ)}{2}\approx40.5$