find the area of the yellow part

In parallelogram $ABCD$ , the red line is the angle bisector of $\angle BAD$ , the blue line is the angle bisector of $\angle CBA$ , the purple line is the angle bisector of $\angle BCD$ and the green line is the angle bisector of $\angle ADC$ . Given that $AB=8$ , $AD=10$ and $\angle BAD=60^\circ$ , find the area of the yellow region. If your answer can be expressed as $\sqrt{a}$ , give the value of $a$ .