# Finding diagonal of Convex Quadrilateral

I know length of a convex quadrilateral's four sides, and one diagonal. Then, how to calculate the other diagonal's length? Here's an example.(Looking for BD)

Using the theorem of cosines we obtain $$BD^2=a^2+d^2-2ad\cos(\alpha)$$
If you know the four sides and a diagonal (e.g.$$AC$$) then you know the area by applying the Heron's formula to the two triangles.