We use Bretschneider's formula:

If a, b, c, and d are the sides of a convex quadrilateral, and s is the
semiperimeter,  and  and  are two opposite angles, 
then the area A of the quadrilateral is given by



First we calculate s with a=10, b=5, c=14.14, d=15,



Then using that and ,




A = 91.89795801035699017470925314054801987941948129813875441889863... cm².

Edwin