Answer
$12.63\ unit^2$
Work Step by Step
1. Based on the given conditions, we have $AO=BO=5$.
2. Use the Law of Cosines, $AB=\sqrt {(5)^2+(5)^2-2(5)(5)cos40^\circ}\approx2.42$ which is the diameter of the semi-circle.
3. The total area is $\frac{1}{2}(5)(5sin40^\circ)+\frac{1}{2}\pi(\frac{2.42}{2})^2\approx12.63\ unit^2$
